Commodity Trade and the Carry Trade:

A Tale of Two Countries∗

Robert Ready†, Nikolai Roussanov‡and Colin Ward§

April 3, 2015

Abstract

Persistent differences in interest rates across countries account for much of the prof-

itability of currency carry trade strategies. The high-interest rate “investment” curren-

cies tend to be “commodity currencies,” while low interest rate “funding” currencies

tend to belong to countries that export finished goods and import most of their com-

modities. We develop a general equilibrium model of international trade and currency

pricing in which countries have an advantage in producing either basic input goods or

final consumable goods. The model predicts that commodity-producing countries are

insulated from global productivity shocks through a combination of trade frictions and

domestic production, which forces the final goods producers to absorb the shocks. As a

result, the commodity country currency is risky as it tends to depreciate in bad times,

yet has higher interest rates on average due to lower precautionary demand, compared

to the final-good producer. The carry trade risk premium increases in the degree of

specialization, and the real exchange rate tracks relative technological productivity of

the two countries. The model’s predictions are strongly supported in the data.

∗We benefited from comments by Andy Abel, Rui Albuquerque, Dave Backus, Gurdip Bakshi, JohnCampbell, Mike Chernov, Ric Colacito, Max Croce, Darrell Duffie, Bernard Dumas, Xavier Gabaix, JeremyGraveline, Robin Greenwood, Tarek Hassan, Burton Hollifield, Urban Jermann, Karen Lewis, Debbie Lu-cas, Hanno Lustig, Don Keim, Brent Neiman, Anna Pavlova, Bryan Routledge, Jose Scheinkman, IvanShaliastovich, Ken Singleton, Rob Stambaugh, Andreas Stathopoulos, Sheridan Titman, Adrien Verdelhan,Jessica Wachter, Amir Yaron, Stan Zin, and audiences at the AFA and ASSA/IEFS meetings, CEPR ESSFMGerzensee, Duke ERID macrofinance conference, Minnesota Asset Pricing conference, Oxford-MAN CurrencyTrading conference, NBER SI, NBIM, SECOR, Texas Finance Festival, SED, WFA, and Wharton. Rous-sanov acknowledges financial support from the Iwanowski Family Research Fellowship and Wharton GlobalResearch Initiative.†Simon School of Business, University of Rochester‡The Wharton School, University of Pennsylvania, and NBER§Carlson School of Management, University of Minnesota

1

1 Introduction

A currency carry trade is a strategy that goes long high interest rate currencies and short low

interest rate currencies. A typical carry trade involves buying the Australian dollar, which

for much of the last three decades earned a high interest rate, and funding the position with

borrowing in the Japanese yen, thus paying an extremely low rate on the short leg. Such a

strategy earns positive expected returns on average, and exhibits high Sharpe ratios despite

its substantial volatility. In the absence of arbitrage this implies that the marginal utility of

an investor whose consumption basket is denominated in yen is more volatile than that of

an Australian consumer. Are there fundamental economic differences between countries that

could give rise to such a heterogeneity in risk?

One source of differences across countries is the composition of their trade. Countries

that specialize in exporting basic commodities, such as Australia or New Zealand, tend to

have high interest rates. Conversely, countries that import most of the basic input goods

and export finished consumption goods, such as Japan or Switzerland, have low interest

rates on average. These differences in interest rates do not translate into the depreciation of

“commodity currencies” on average; rather, they constitute positive average returns, giving

rise to a carry trade-type strategy. In this paper we develop a theoretical model of this

phenomenon, document that this empirical pattern is systematic and robust over the recent

time period, and provide additional evidence in support of the model’s predictions for the

dynamics of carry trade strategies.

The fact that carry trade strategies typically earn positive average returns is a manifes-

tation of the failure of the Uncovered Interest Parity (UIP) hypothesis, which is one of the

major longstanding puzzles in international finance. A longstanding consensus in the inter-

national finance literature attributed all of the carry trade average returns to conditional risk

premia, finding little evidence of non-zero unconditional risk premia on individual currencies

throughout most of the twentieth century (e.g. see Lewis (1995)). Consequently, much of

the literature has focused on explaining the conditional currency risk premia by ruling out

asymmetries (e.g., Verdelhan (2010), Bansal and Shaliastovich (2012), Colacito and Croce

(2012)). However, Lustig, Roussanov, and Verdelhan (2011) show that unconditional cur-

2

rency risk premia are in fact substantial; indeed, they account for between a third and a half

of the profitability of carry trade strategies, Hassan and Mano (2014) provide evidence that

carry trade profits are in fact primarily driven by unconditional differences in currency risk-

premia across countries.1 Lustig, Roussanov, and Verdelhan (2011) argue that these returns

are compensation for global risk, and the presence of unconditional risk premia implies that

there is persistent heterogeneity across countries’ exposures to common shocks. In this paper

we uncover a potential source of such heterogeneity.2

We show that the differences in average interest rates and risk exposures between coun-

tries that are net importers of basic commodities and commodity-exporting countries can

be explained by appealing to a natural economic mechanism: trade costs.3 We model trade

costs by considering a simple model of the shipping industry. At any time the cost of trans-

porting a unit of good from one country to the other depends on the aggregate shipping

capacity available. While the capacity of the shipping sector adjusts over time to match the

demand for transporting goods between countries, it does so slowly, due to gestation lags

in the shipbuilding industry. In order to capture this intuition we assume marginal costs of

shipping an extra unit of good is increasing - i.e., trade costs in our model are convex. Con-

vex shipping costs imply that the sensitivity of the commodity country to world productivity

shocks is lower than that of the country that specializes in producing the final consumption

good, simply because it is costlier to deliver an extra unit of the consumption good to the

commodity country in good times, but cheaper in bad times. Therefore, under complete

financial markets, the commodity country’s consumption is smoother than it would be in the

1See also Bakshi, Carr, and Wu (2008), Campbell, Medeiros, and Viceira (2010), Koijen, Pedersen,Moskowitz, and Vrugt (2012), and Lustig, Roussanov, and Verdelhan (2013) for additional empirical evi-dence. Theoretical models of Hassan (2013) and Martin (2011) relate currency risk premia to country size.Stathopoulos, Vedolin, and Mueller (2012) assume an exogenous source of heterogeneity in a multi-countrymodel with habit formation.

2A number of patterns of heterogeneous risk exposures have been documented empirically. In a pioneeringstudy, Lustig and Verdelhan (2007) show that carry trade risk premia line up with loadings on the U.S.aggregate consumption growth; Lustig, Roussanov, and Verdelhan (2011) and Menkhoff, Sarno, Schmeling,and Schrimpf (2012) link these risk premia to covariances with the global stock market and foreign exchangerate volatility shocks, respectively, while Lettau, Maggiori, and Weber (2013) show that high average returnstrategies in currency and commodity (as well as equity) markets perform particularly poorly during largeU.S. stock market declines.

3Trade costs have a long tradition in international finance: e.g., Dumas (1992), Hollifield and Uppal(1997). Obstfeld and Rogoff (2001) argue that trade costs hold the key to resolving several major puzzles ininternational economics.

3

absence of trade frictions, and, conversely, the commodity importer’s consumption is riskier.

Since the commodity country faces less consumption risk, it has a lower precautionary saving

demand and, consequently, a higher interest rate on average, compared to the country pro-

ducing manufactured goods. Since the commodity currency is risky - it depreciates in bad

times - it commands a risk premium. Therefore, the interest rate differential is not offset on

average by exchange rate movements, giving rise to a carry trade.

We show empirically that sorting currencies into portfolios based on net exports of finished

(manufactured) goods or basic commodities generates a substantial spread in average excess

returns, which subsumes the unconditional (but not conditional) carry trade documented by

Lustig, Roussanov, and Verdelhan (2011). Further, we show that aggregate consumption

of commodity countries is less risky than that of finished goods producers, as our model

predicts.

The model makes a number of additional predictions that are consistent with salient

features of the data. Commodity-currency carry trade returns are positively correlated with

commodity price changes, both in the model and in the data (we provide evidence using

an aggregate commodity index, which complements the result obtained by Ferraro, Rossi,

and Rogoff (2011) who use individual currency and commodity price data). Moreover, the

model predicts that conditional expected returns on the commodity-currency carry trade

are especially high when global goods markets are most segmented, i.e. when trade costs

are particularly high. We show that a popular measure of shipping costs known as the

Baltic Dry Index (BDI) forecasts unconditional carry trade returns (but not their conditional

component). Our model also rationalizes the evidence of carry trade predictability with a

commodity price index documented by Bakshi and Panayotov (2013), since commodity prices

are typically high in the model during booms, when trade costs are also high.

4

2 Model

2.1 Setup

There are two countries each populated by a continuum of ex ante identical households

endowed with time-separable preferences over the same consumption good. Both countries’

representative households have CRRA preferences with identical coefficients of relative risk

aversion γ and rates of time preference ρ. Time is continuous, and all households are infinitely-

lived.

The countries are spatially separated so that transporting goods from one country to the

other incurs trade costs, although we abstract from shipping costs for the basic commodity

for tractability.4 The “commodity country” has two production technologies available: one

technology for producing the final (consumable) good; the other, for producing basic com-

modity which is an input required for production of the final good. The “producer country”

only has one technology to produce the final good. Firms in both industries and in both

countries are competitive.

The commodity country has a linear technology for producing the commodity that is

either used domestically or exported to the producer country,

yct = zctlct,

where lc is a local non-traded input (this can be thought of labor or land) and zc is its

productivity.

The commodity country also has the final-good production function

ycpt = zcpt(yct − xt)αl1−αcpt , (1)

where zcp is a productivity level and x is the quantity of commodity exported, while lcp is the

local non-traded input. The latter is supplied inelastically in the amount of one unit, but is

4Although introducing such costs does not alter the main qualitative predictions of the model; see, Ready,Roussanov, and Ward (2013).

5

perfectly substitutable between the two sectors, so that lc + lcp = 1.

Since the producer country imports the commodity at no cost and there is only one pro-

duction technology competing for the local resources, the same production function implies

its output of the final good is given by

ypt = zptxt, (2)

where zp is its productivity level. We assume that the producer country has an absolute

(as well as comparative) advantage in producing the final good:

zpt > zct (almost surely).

Given this assumption, in the absence of trade frictions it would be optimal for the two

countries to specialize, so that the commodity country only produces the basic commodity

and exports all of it to the producer country, where all production of the final good is

concentrated. However, most commodity-producing countries do produce at least some of

the goods they consume domestically, presumably because some of these goods are too costly

to import from countries that produce them more efficiently, and in fact some consumption

goods are entirely non-traded. We model such trade frictions by extending the classic variable

iceberg cost of Backus, Kehoe, and Kydland (1992), where each unit of the final (consumable)

good shipped from the producer country to the consumer country loses a fraction

τ(Xt, zpt) =κ

2

Xt

zpt,

which depends on the total amount of goods exported from the producer country to the

commodity country, Xt, and the productivity in the final-good producer country zpt. The

latter is meant to capture the dependence of trade frictions on the various short-run factors,

such as available shipping capacity that cannot be adjusted quickly and is likely procyclical,

as well as costs of financing trade that may be counter-cyclical.5 The assumption that the

5Here shipping capacity is perfectly aligned with producer-country productivity. This assumption is notcritical in generating the results: we relax it by allowing the two to be cointegrated in Ready, Roussanov, and

6

marginal cost of trade increases in the amount of exports is consistent with evidence on the

various components of these costs. Hummels (2007) discusses evidence on evolution of trade

costs over time and notes that despite a decline in freight costs actual trade costs may not

decrease, for example as increasing amount of trade leads to greater congestion in ports, etc.

Kalouptsidi (2014) and Greenwood and Hanson (2015) document substantial variation in

freight costs due to gestation lags in the shipping sector and, consequently, global shipping

capacity that is inelastic in the short run. Arkolakis (2010) shows that micro-level evidence

is consistent with increasing marginal cost of exporting for individual firms.

The presence of trade frictions implies that the real exchange rate, i.e. the relative price

of the same consumption bundle in the two countries, is not equal to unity. We denote this

real exchange rate, expressed in the units of the producer country consumption basket per

one unit of the commodity country consumption, by St.

Let pt and p∗t denote the price of the basic commodity in the units of the numeraire

consumption good in the commodity and the producer countries, respectively. Since trans-

porting the commodity between the two countries is costless, the law of one price holds, as

the prices in the two countries are equated up to the exchange rate:

pt =p∗tSt. (3)

2.2 Production

Given the structure of the production technologies, all firm decisions are static. Therefore,

we can consider the intratemporal production decisions at a given point in time t without

making specific assumptions on the dynamics of the exogenous state variables or considering

the consumer problem. In this section we suppress all of the time subscripts for brevity.

Ward (2013). While we use “trade costs” and “shipping costs” interchangeably, in principle trade costs includea broader category of frictions than the monetary cost of freight. These could include the time delays dueto port congestion, tariffs and non-tariff barriers to trade, and local distribution costs. More generally, thisincludes the idea that some goods are so prohibitively expensive to ship that they are essentially nontraded.An alternative would be to endow each country’s consumers with a stronger preference for domesticallyproduced consumption goods relative to foreign one, as used in international macroeconomics, e.g. by Backus,Kehoe, and Kydland (1994), and in the context of international asset pricing by, e.g., Pavlova and Rigobon(2007), Colacito and Croce (2010), and Stathopoulos (2011). We retain the classic BKK specification largelyfor tractability.

7

In each period, the commodity country firms in the commodity sector solve

maxlc

pzclc − wlc ⇒ w = pzc,

that must be satisfied for the price of local nontraded input w. The final-good sector firms

solve

maxx,lcp

zcp(zclc − x)αl1−αcp − p(zclc − x)− wlcp

subject to the constraint that lc + lcp = 1. The first-order conditions of this problem imply

that

α

1− αzclcp = zclc − x (4)

⇒ lc = α + (1− α)x

zc, (5)

lcp = (1− α)

(1− x

zc

). (6)

This implies that the fraction of labor directed to commodity production increases with

the amount of commodity exports x. The maximum (lc = 1) is reached when all of the

commodity endowment is exported (x = zc). The same set of necessary conditions (for an

interior solution) imply that the price of the commodity in the commodity country is given

by

p = αzcp

(1− ααzc

)1−α

. (7)

The commodity price p is a decreasing function of commodity endowment and an in-

creasing function of the domestic final-good productivity. In particular, the combination of

Cobb-Douglas and linear technologies imply that foreign demand for the commodity does

not have a direct effect on the domestic price. However, it does determine the amount of the

commodity exported to the producer country.

The producer country’s final-good firm solves

maxx

zpx− p∗x (8)

⇒ zp = p∗. (9)

8

Consequently, the goods-market no-arbitrage condition (3) implies a relationship between

the real exchange rate and the relative productivities in the final-good sectors of the two

countries:

S =p∗

p=

zpαzcp

(1− ααzc

)α−1

, (10)

which must be satisfied as long as both countries simultaneously use the commodity input to

produce the final consumption good. In particular, the commodity currency appreciates in

“good times” from the perspective of the final-good producer; that is, when its productivity

improves (or when the commodity country’s final-good productivity worsens).

2.3 Dynamics

We assume the shocks experienced by the producer country’s final-good productivity are

permanent, its evolution following a standard geometric Brownian motion:

dzptzpt

= µdt+ σdBt.

To ensure stationarity of the model, we assume the commodity country’s productivity

dzcpt is cointegrated with the producer country’s productivity and follows a general diffusion

process. Its process is specified (explicitly in the Appendix) to ensure stationarity of the

relative productivity:

zt.=zcptzpt

.

The assumption of comparative advantage requires zt < 1; we further restrict its domain by

requiring zt > z for some z > 0, so that the commodity country can always produce the final

good. We assume that the relative productivity process follows a regulated Brownian motion

dzt = µztdt+ σzdBzt − dUt + dLt,

where Ut and Lt are continuous, non-decreasing processes, and dBzt is independent of dBt.

Lt only increases when zt = z and Ut only increases when zt = 1.6 The resulting cointe-

6Regulated Brownian motions have been previously used in the international economics literature to modelexchange rate dynamics in the presence of a target zone; see, Svensson (1991) and Froot and Obstfeld (1991).

9

gration relation can be interpreted as a reduced-form representation of an economy where

both countries independently, and exogenously, innovate to improve their technologies that

produce the final good, but the producer country always leads the commodity country in

technological advancement. We set µzt = σ2z/zt. The specification of the drift can be thought

of as having the commodity country adopt ideas and technologies from the producer country,

thus allowing it to catch up in technological advancement, with the effect being greater dur-

ing greater differences in relative productivity. In effect, the processes dzcpt and dzpt become

more correlated when zt nears one. This setup makes the relative ratio of productivities vary

independently of the absolute level of productivity of the producer country, zpt, which is a

feature of the model that makes it particularly tractable.

Finally, we assume that the productivity in the commodity sector is constant, zct = zc,

so as to demonstrate clearly the role of the relative productivity in the final-good sector, as

well as to make the model more tractable.7 Under this assumption we can define a constant

as a function of zc, φ(zc) = α(

1−ααzc

)1−α, so that the commodity price (in the units of the

commodity country currency) is simply pt = φ(zc)zcpt.

2.4 Complete markets and consumption risk sharing

In order to emphasize that our mechanism does not rely on any financial market imper-

fections, we consider consumption allocations under complete markets. This is a standard

benchmark in international finance, and is reasonable at least when applied to developed

countries.8 The main implications of our model do not hinge on the complete markets as-

sumption, but the standard setting lends both transparency and tractability to the analysis.

Under complete markets, the equilibrium allocation is identical to that chosen by a central

We describe the process in more detail in the Appendix.7More generally commodity supply can be modeled as a stochastic endowment cointegrated with global

productivity (i.e., zp). Such a cointegrated relationship can be interpreted as a reduced form representationof an economy where supply of the commodity is inelastic in the short run (based on the currently exploredoil fields, say) but adjusts in the long run to meet the demand by the final-good producers (e.g., as newfields are explored more aggressively when oil prices are high). We solve a version of such model in Ready,Roussanov, and Ward (2013).

8For example, Fitzgerald (2012) estimates that risk-sharing via financial markets among developed coun-tries is nearly optimal, while goods markets trade frictions are sizeable.

10

planner for a suitable choice of a (relative) Pareto weight λ. The planner’s problem is

V (zpt, zcpt) = maxXs

Et[∫ ∞

t

e−ρ(s−t)(c1−γcs − 1

1− γ+ λ

c1−γps − 1

1− γ

)ds

],

where commodity-country consumption ccs = ps(zc−xs)+Xs(1− κXs2zps

) and producer-country

consumption cps = zpsxs − Xs, subject to the constraints (7) and (10) imposed by the

production side of the economy (the latter are equivalent to including choice over xs and lcs

in the planner problem, since firms act competitively). As before, because the production

economy here is essentially static, the planning problem collapses to a sequence of one-period

problems and we henceforth ignore time subscripts.

The first-order condition of the planner’s problem, which holds state-by-state for all t,

implies that

c−γc

(1− κX

zp

)− λc−γp = 0. (11)

Since the real exchange rate (here defined in the units of the producer currency per one

unit of the commodity currency) is the relative price of consumption in the two countries, it is

proportional to the ratio of marginal utilities of the two countries’ representative consumers:

S =1

λ

(cccp

)−γ. (12)

The combined equations (10) and (11) show how the exchange rate is jointly determined by

the production and the consumption sides of the economy. Equation (10) states that the

marginal product of the commodity is equated between the two countries, once expressed in

the units of one of the country’s currency (or consumption). Consequently, the real exchange

rate must equal the ratio of the two countries’ productivities (up to a constant):

S ∝ 1

z. (13)

By using Ito’s lemma for regulated processes (see Harrison (1985, p.82)), the dynamics

of the exchange rate under µz = σ2z

zare

dS

S= −dz

z+dz2

z2= − z

z2dL+ zdU − σz

zdBz. (14)

11

Our selection of the drift of the process z gives the model a nice feature, which is sum-

marized in the next lemma (and proved in the Appendix).

Lemma 1 (Real exchange rate follows a martingale). If µzt = σ2z/zt then the growth of the

real exchange rate is a martingale:

Et[dS

S

]= 0.

Indeed, that the real exchange rate follows a martingale is consistent with empirical evi-

dence that exchange rate changes are essentially unforecastable (see, e.g. Adler and Lehmann

(1983), Meese and Rogoff (1983)).

Equation (11) states that the relative value of the consumption good in two countries

is equated up to the marginal cost of transporting it from the producer country to the

commodity country. Consequently, the real exchange rate is proportional to the marginal

value of one unit of the final good that has been transported from the producer to the

commodity country, as is generally the case in one-good models with trade costs (e.g., see

Dumas (1992), Hollifield and Uppal (1997), Verdelhan (2010)):

S =1(

1− κXzp

) . (15)

The first-order condition in (11) combined with the law of one price for commodities in

(10) gives an explicit solution for final-good exports X:

X =

(1− p

zp

)zpκ

=1

κ(zp − φ(zc)zcp) . (16)

This expression is very intuitive: it shows that exports of the final good are increasing

(linearly) in the producer-country labor productivity, and decreasing in the final-good pro-

ductivity in the commodity country. The trade cost scales down final good exports and

therefore drives a wedge between the two countries’ consumptions. The magnitude of this

wedge depends on the relative productivity of final-good production, z, and using the first-

12

Figure 1: Consumption wedge

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5

1

1.5

2

2.5

3

3.5

z

order conditions we can formally define this consumption wedge

ω(z).=cpcc

=

(1− κX

zp

λ

)− 1γ

=

(p

λzp

)− 1γ

=

(φ(zc)

λz

)− 1γ

. (17)

The consumption wedge measures the extent to which the producer country bears a larger

share of aggregate consumption and also the risk associated with it. Because in equilibrium

the producer country’s consumption will be a nonlinear, scaled version of the commodity-

country’s consumption, the producer country will have a relatively more variable consumption

stream. On average, if long-run consumption growth rates are equal between the two coun-

tries, greater demand for precautionary savings will lead the producer country to have a

relatively lower risk-free rate.

A related comment is that because the real exchange rate is positively related to the con-

sumption wedge, S = 1λω(z)γ, the real exchange will comove positively with it and thus will

depreciate in “bad times” for the producer country, when its relative aggregate consumption

share declines.

13

Solving for equilibrium commodity exports x gives

x (zp, z) =pzcω(z) +X +X

(1− κ

2Xzp

)ω(z)

zp + pω(z),

which can be used to compute the consumption allocations:

cc = zpzcφ(zc)z + 1

2κ(1− φ(zc)z)2

1 + ω(z)φ(zc)z(18)

and

cp = ω(z)cc.

Commodity country consumption cc comes from two sources: the first is domestic pro-

duction of the final good, while the second consists of imports of the final good from the

producer country. When z decreases, the main source of consumption for the commodity

country shifts from domestic production to imports. Additionally, the consumption wedge

increases, as the producer country bears an increasingly greater share of aggregate risk. This

widening of the consumption wedge can be seen as a simple form of the “Dutch Disease”:

as the ‘world’ price of the commodity rises, driven by the increase in foreign productivity

relative to its domestic level, commodity production and exports crowd out domestic pro-

duction; however, trade frictions imply that the rising imports of consumption goods are not

sufficient to compensate for the decline in local production for domestic consumers.

Conversely, as z increases towards its upper limit of unity, commodity exports x decline,

raising domestic production of the final good in the commodity country and shrinking the

consumption wedge. We rely on the following lemma and discuss its proof in the Appendix:

Lemma 2. There exists a fixed point z∗c = H(z∗c ) given parameters α, λ, κ, γ, and z¯

where

H(z∗c ).= max

zc

1

κ(1− φ(zc)z

¯)

(1 +

1

2(1 + φ(zc)z

¯)

(φ(zc)

λz¯

)− 1γ

).

And therefore x (zp, z) ≤ z∗c for all zp > 0 and all z ∈ (z¯

,1).

Thus the commodity-export ratio x/zc is always less than or equal to one. Furthermore,

14

we hereon restrict attention to cases where zc > z∗c and will simply then define a constant φ∗

as a member of this set of satisfactory constants: φ∗ ∈ {φ(zc)|zc > z∗c}. With this restriction

we have x < zc always and φ∗ < 1.

2.5 Import ratios

While our model features complete specialization, in the sense that each country only exports

one type of good, the degree to which a country is an importer of final goods and an exporter

of commodities, and vice versa, relative to its output, varies over time. This degree can be

quantified by measuring imports of the two types of goods relative to output, with the view

towards testing model’s predictions in empirical work. Define the import ratio for a given

country as

Net Imports of Finished Goods + Net Exports of Basic Goods

Output.

where we normalize the trade quantities in the numerator by consumption here, then we have

the following:

• Commodity-country import ratio: IRc.= XS+xpS

ycpS

• Producer-country import ratio: IRp.= −

(X+xpSyp

)The spread of the log of these ratios (IRc − IRp) is plotted in Figure 6. The ratios do

not converge to zero when z approaches one because the producer country needs to import

the commodity to have positive consumption. This ratio is an easily measurable empirical

quantity. As a country becomes relatively more efficient at producing the final good, it

becomes a net exporter of final goods, and has a lower and possibly even negative import

ratio. On the other hand, as a country becomes more efficient at producing commodities,

relative to its production capabilities of producing the final good, its import ratio rises. The

spread between the two country’s import ratios acts as a measure of relative productivity

and comparative advantage, which in turn is a measure of the degree to which the country

with the lower import ratio bears aggregate risk.

15

Figure 2: Import ratio spread: log(IRc − IRp)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

z

It follows from our definitions of final-good outputs in (1) and (2), equation (3), and the

first-order condition in (5) that global output in units of the producer country’s final good

equals Y = zpzc. Consequently, z has no effect on this quantity, only its spatial distribution

of output across countries. However, countries’ productivities and industrial outputs co-move

differently with global output, as shown in the following Lemma.

Lemma 3. The change in productivity of the producer country covaries more with the change

in global output, Y = zpzc, than does the commodity country’s change:

Et [dzp · dY ] = σ2z2pzcdt > zσ2z2

pzcdt = Et [dzcp · dY ]

Because global final-good output is determined relatively more by the producer country, as

it has greater final-good productivity, its productivity is naturally going to be more correlated

with global output. We relegate the discussion on the empirical support of this prediction to

Section 3.3.

16

2.6 Asset pricing implications

The definition of stochastic discount factor (SDF) for the producer country is standard and

with an application of Ito’s lemma for regulated processes has the dynamics

dπpπp

= −ρdt− γ dcpcp

+1

2γ(1 + γ)

dc2p

c2p

− γ 1

cpdL+ γ

1

cpdU,

where the terms of dL and dU will be referred to in what follows as the “regulator terms”.

The commodity country’s SDF follows from our complete markets assumption, which

allows it to be usefully rewritten in terms of S and cp.

πc = e−ρtc−γc = e−ρt(

cpω(z)

)−γ= e−ρtc−γp Sλ

⇒ dπcπc

= −ρdt+dS

S− γ dcp

cp+

1

2γ(1 + γ)

dc2p

c2p

− γ dSS

dcpcp− γ 1

cpdL+ γ

1

cpdU,

where we suppressed the regulator terms of dS/S as they appear in (14) and exploited the

relationship Sλπp = πc.

Noting that the producer-country consumption regulator terms conveniently cancel out

when differencing, the interest rate differential between the two countries is then given by

(rfc − rfp )dt = −Et[dπcπc

]+ Et

[dπpπp

]= −Et

[dS

S

]+ γEt

[dS

S

dcpcp

], (19)

where the first term is the expected depreciation of the commodity currency and the second

term is the risk premium. The latter equation can be written as

(rfc − rfp )dt+ Et[dS

S

]= γEt

[dS

S

dcpcp

]︸ ︷︷ ︸

Risk premium

Because the real exchange rate follows a martingale, the risk premium simply equals the

interest rate differential, and, aside from the specification of standard CRRA preferences, is

17

Figure 3: Carry trade risk premium

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2x 10

−3

z

%

independent of the other features of the model. The risk premium is given by

γEt[dS

S

dcpcp

]= γσ2

z

1

z2

[1

2κ(1− φ∗z)2

zcφ∗z + 1

2κ(1− φ∗z)2

(1 + φ∗z)

1− φ∗z−

1− 1γ

1 + φ∗zω(z)

]dt. (20)

In the special case of log utility, the risk premium, interest rate differential, and difference

in the import ratio, can be signed analytically.

Proposition 1 (Risk premium, interest rate differential and import ratio). If the conditions

of Lemma 2 above are satisfied and γ = 1, then

1. the risk premium and the interest rate differential are positive for all z

2. the spread of the import ratios ∆IR.= IRc − IRp is decreasing in z

3. if α ∈ [0, 0.8651) and zc > max{ 2√5−1

, z∗c}, then the risk premium and the interest rate

differential are decreasing in z. Thus, the spread between the import ratios is positively

related to the currency risk premium and the interest rate differential.

The conditions required for the positivity of the risk premium, in addition to log utility,

simply ensure that some quantity of the basic commodity is always retained to be used as

input in domestic production in the commodity country. The second is a technical condition

18

that is easily satisfied for reasonable parameter values: (i) a Cobb-Douglas labor share in

final-good production over 0.1349 and (ii) a large enough quantity of commodity production

to satisfy Lemma 1 or a simple value of 2√5−1

.9

Both the interest rate differential and the risk premium are closely related to the import

ratio. Figure 4 demonstrates that both are increasing as z falls, while the dispersion between

the two countries’ import ratios rises. Therefore, the behavior of the conditional currency

risk premia can be captured by the dispersion between the import ratios of the commodity

country and producer country.

Figure 4: Relationship between interest-rate differential, risk premium, and import ratio

0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2x 10

−3

z

IRD (%)

0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2x 10

−3

z

Risk premium (%)

0.2 0.4 0.6 0.8 11

2

3

4

5

6

7

z

log(IRc−IR

p)

The risk premium is increasing in the consumption wedge, which captures the degree of

endogenous risk sharing between the two countries. Risk sharing is weakest when the trade

costs are high and, consequently, the consumption wedge is large. Figure 5 plots the currency

risk premium against the average trade cost, illustrating the strong monotonic relationship

between the two: high trade costs imply a high risk premium.

2.7 Summary of implications

The qualitative implications of the above proposition can be summarized as a set of predic-

tions for the risk and return properties of exchange rates.

1. The final-good-producing country bears more aggregate risk. Therefore, it has a larger

precautionary demand and lower interest rates, on average, than the commodity-

producing country. (Proposition 1)

9These conditions are described in the Appendix.

19

Figure 5: Carry trade risk premium

0

0.2

0.4

0.6

0.8

1

1.2x 10

−3

Average trade cost

%

2. The commodity earns a risk premium, giving rise to a carry trade. (Proposition 1)

3. The interest rate differential and the commodity currency risk premium are both in-

creasing in spread between the import ratios of the two countries. (Proposition 1)

4. The change in the productivity of the producer country is more correlated with global

output than is the commodity country’s. (Lemma 3)

5. Real exchange rates and interest rate differentials between commodity and producer

country currencies are proportional to the ratio of productivities in the countries’ final

goods producing sectors. (Equation 12)

6. A widening of the productivity wedge between the producer country and the commodity

country implies high shipping costs and a lower degree of international risk sharing.

Therefore conditional expected carry trade returns are positively correlated with trade

costs. (Proposition 1 and Equation 16)

Our model of exchange rate determination is deliberately simple and meant to highlight

the mechanism leading to a carry trade: specialization combined with non-linear shipping

costs. The model nevertheless makes a rich set of qualitative predictions, which we now

evaluate empirically.

20

2.8 Discussion of implications

In deriving the model’s implications described above we rely on the assumption of complete

markets for tractability. This assumption is admittedly extreme, and is likely to lead to

counterfactual predictions, in particular regarding the behavior of aggregate consumption

growth. In particular, one of the classic puzzles of international finance going back to Backus

and Smith (1993) is the fact that differences betwen countries’ consumption growth rates

tend to be only weakly correlated with real exchange rate changes, and often with the wrong

sign. This puzzle does not in itself invalidate our model’s mechanism: it is relatively stan-

dard in the literature to depart from the assumption of complete markets by considering

economies with limited participation, where some but not all households share risks inter-

nationally while other ”inactive” households do not participate in financial markets at all -

e.g. Alvarez, Atkeson, and Kehoe (2002), Hassan (2013), and Ramanarayanan and Cociuba

(2011). In particular, Hassan (2013) shows that the interest rate differentials that translate

into risk premia due to differences in countries’ effective consumption risk generalize to such

a segmented market economy where only the “active” investors’ consumption matters for

risk premia.10 There is no reason to expect that such an argument would not carry over to

our setting, albeit at a cost of substantially reduced tractability.

The key prediction - that the commodity country currency is riskier - follows directly

from the goods-market no-arbitrage condition (3) and the fact that the producer country

productivity is more important for global output (and therefore consumption). However,

predictions about relative volatility of aggregate consumption growth are likely to be more

sensitive to market structure. In particular, they are likely to be especially counterfactual

for the cases of emerging commodity countries, which are likely to be far from the complete

markets benchmark as few they are not sufficiently financially developed to allow a large

fraction of consumers to share risk internationally. In fact, this conforms with a standard

intuition that (developing) commodity countries are “riskier” - this may be the case if terms

of trade are sufficiently volatile and markets sufficiently segmented to allow for very little

insurance.

10Alternatively, the Backus-Smith puzzle could be resolved within the representative-agent setting undernon-separable preferences (e.g., Colacito and Croce (2011), Stathopoulos (2011)).

21

Consequently, we do not emphasize the model’s predictions regarding aggregate consump-

tion volatility in what follows and instead focus on the role of relative productivity. This may

be particularly important when considering emerging countries, since they are the least likely

to exhibit a high degree of international risk sharing due to limited financial development

stemming from the lack of sufficient investor protection, capital controls, and other barriers

to financial trade. In fact, emerging commodity countries are often thought of as exposed to

more (rather than less) risk precisely because they are unable to buffer terms of trade shocks

via trade in financial claims in the way that more developed countries might (e.g., Norway).

Relative productivity is an important object in international economics. In fact, our

model’s relation between the productivity differential and the real exchange rate resembles

the classic Balassa-Samuelson effect, which is a statement that the relative price of nontraded

(or relatively less traded) goods and, therefore, real exchange rate, is higher for the countries

with higher labor productivity. This effect relies on the existence of a perfectly traded good

and perfectly elastic substitution of labor between sectors. In the context of our model

the basic commodity is the freely traded good and the commodity country always has the

advantage at producing it, but labor productivity differs across sectors. Nevertheless, the

Balassa-Samuelson effect can still be seen at work in the sense that the commodity country’s

price of the final consumption good is always higher than in the producer country, since it is

more costly to either produce it in or import it into the commodity country (and consequently

marginal utility of consumption is higher). The effect of labor productivity is the reverse of

that in the Balassa-Samuelson hypothesis because it is allowed to vary across sectors, so that

when productivity in the final good sector rises in the commodity country it actually shifts

labor out of the more productive export sector and into the (less traded) consumption good,

lowering its price and therefore the real exchange rate. The potential role of differences in

labor productivity across sectors that are highlighted in our model could be one of the reasons

why empirical evidence for the Balassa-Samuelson effect is somewhat mixed (e.g. see Rogoff

(1996) and references therein).

Since our model features a single consumable good and a cost to transporting this good

between countries it shares some elements with the classic models of international finances

such as Dumas (1992). In these models exchange rates vary in a region where no trade

22

occurs due to the proportional trade cost, driven by shocks to capital productivities in the

(ex ante symmetric) countries. The less productive country (importing the good) has a higher

interest rate and its currency earns a positive risk premium, but the bulk of the interest rate

differential is driven by the expected currency depreciation while the risk premium is generally

small and behaves highly nonlinearly. In fact Hollifield and Uppal (1997) show that a model

of this class cannot satisfy the Fama (1984) condition that the volatility of the currency

risk premium must be larger than the volatility of expected currency depreciation in order

to reproduce the forward premium puzzle. This condition is satisfied trivially in our model

since the real exchange rate is a martingale, and consequently the risk premium accounts for

the entirety of the interest rate differential.

3 Empirical evidence

3.1 Data

Following Lustig, Roussanov, and Verdelhan (2011) we use forward and spot exchange rates

to construct forward discounts (approximately equal to the interest rate differentials by the

covered interest parity relation) and excess returns on currencies. Denoting log forward

exchange rate one month ahead ft = logFt and log spot exchange rate st = logSt, both

expressed in units of foreign currency per one U.S. dollar, the forward discount is equal to

the interest rate differential: ft− st ≈ i?t − it, where i? and i denote the foreign and domestic

nominal one month risk-free rates.

The log excess return rx on buying a foreign currency in the forward market and then

selling it in the spot market after one month is then given by

rxt+1 = ft − st+1,

while the arithmetic excess return is given by

Rxt+1 =FtSt+1

− 1.

23

Data is provided by Barclays and Reuters and is available via Datastream. We use monthly

series from February 1988 to April 2013.11

We use two samples in our analysis. The sample of all 35 developed and emerging coun-

tries includes: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Euro area,

Finland, France, Germany, Greece, Hungary, India, Indonesia, Ireland, Italy, Japan, Kuwait,

Malaysia, Mexico, Netherlands, New Zealand, Norway, Philippines, Poland, Portugal, Sin-

gapore, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, United

Kingdom. The sub-sample of 21 developed-country currencies includes: Australia, Austria,

Belgium, Canada, Denmark, Euro, Finland, France, Germany, Greece, Ireland, Italy, Japan,

Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom.

3.2 Unconditional Average Excess Returns

Table 1 shows U.S. dollar average returns and forward discounts on the nine most actively

traded currencies, collectively known as the G10 countries (the tenth currency being the U.S.

dollar itself), over our sample period. Following Lustig, Roussanov, and Verdelhan (2011), we

compute the average forward discount prior to 1995 and the returns after 1995. The German

Deutschmark forward discount and the excess return to investing in Deutschmark forward

contracts prior to 1999 are spliced with the euro variables post-1999. The table is sorted from

low average returns to high average returns. What is immediately apparent is that the high

return countries tended to have unconditionally high forward discounts, consistent with the

unconditional carry trade strategy documented in Lustig, Roussanov, and Verdelhan (2011).

Interestingly, this relation between average forward discounts and excess returns is not a

perfectly monotonic one, in that some low return countries have high discounts. This is not

necessarily surprising since factors other than expected returns (e.g. expected inflation) can

11While Lustig, Roussanov, and Verdelhan (2011) start their sample in 1983, very few currencies haveforward discounts available in the first few years of the sample, as a number of countries, including Australiaand New Zealand, undergo transition from fixed to floating exchange rates during this period. The lattercountries have forward discounts available starting in 1985, but these display patterns suggesting episodesof extreme illiquidity, such as large bid-ask spreads and violations of covered interest parity relation (CIP)before 1988. Finally, the Plaza Accord of September 22, 1985 led to a large but gradual appreciationof the Deutschmark, the French Franc, and the Japanese Yen over the course of 1986 and 1987. Sincethese movements were largely predictable by investors it appears natural to consider unconditional strategiesincluding these currencies starting in 1988.

24

Table 1: G10 Currency Average FX Returns and Discounts

Country Excess Return Forward DiscountJapan -1.97 -2.70

Switzerland -0.32 -1.53Germany/Euro 0.11 -0.15

Sweden 0.80 1.37United Kingdom 0.92 1.81

Canada 1.66 0.65Norway 1.99 1.81

Australia 4.02 2.71New Zealand 4.06 3.08

Average annualized forward discounts prior to 1995 and and excess returns (without accounting for transac-

tion costs) after 1995 for the ”G-10” currencies from the perspective of a U.S. dollar investor. Germany/Euro

is calculated based on the German Deutschmark prior to 1999 and the Euro post 1999. Data are monthly

forward contracts from 1988 to 2012 available via Datastream.

have an effect on nominal interest rates, and therefore forward discounts.12 It is clear, how-

ever, that the countries with low returns tend to be countries with advanced manufacturing

economies which are also relatively resource poor. Indeed, the entire top half of the table:

Germany, Japan, Sweden, Switzerland, and the UK all fit this description to some degree. In

contrast, the high return countries on the bottom half of the table tend to be large exporters

of either oil (Canada and Norway) or other base agricultural or mineral commodities (New

Zealand and Australia).

3.3 Import Ratios, Interest Rates, and Currency Excess Returns

In order to classify countries based on their exports we utilize the U.N. COMTRADE

database of international trade flows. We use the NBER extract version of this data, available

for years 1980-2000, we augment it with the original COMTRADE data for years 2001-2012

following the same methodology. The two goods in the model are a basic good, which is used

as an input in production, and a final good, which is used in consumption. While this suggests

12Pairwise average currency returns are only marginally statistically different from zero due to the substan-tial noise in bilateral exchange rate movements, consistent with evidence in Bakshi and Panayotov (2013);however, aggregating currencies into portfolios (e.g., long bottom four, short top four) reduces idiosyncraticnoise and ensures robustly statistically significant average returns (as detailed in Data Appendix Table A-1).

25

a potential classification of goods as either “input” or “final” goods, there are many goods for

which this classification struggles to conform to the intuition of the model. The important

mechanism in the model hinges on the extra trade costs associated with shipping complex

produced goods back to the commodity exporter rather than the specific use of the goods as

consumption or input. For instance, New Zealand is a large exporter of many agricultural

commodities, some of which (such as butter) are in their final consumable form. Likewise,

New Zealand imports a large amount of sophisticated construction equipment which is pro-

duced using basic commodities (e.g., metals, energy) as an input. However, in the context of

the model, a complex piece of construction equipment seems more closely related to the final

good rather than the basic good, while butter is a better representation of the basic good.

Moreover, the specialization assumption in the model implies that the production process in

the producer country cannot be easily replicated in the commodity country, suggesting a high

level of complexity for the final good. Therefore to be consistent with the model mechanism

we classify goods as a basic good (i.e. a commodity) or a complex manufacturing good based

on their 4-digit SITC codes. The classifications at the 2-digit level are in the appendix (Table

A-2), and the full classification is available upon request.

In order to test the model’s predictions we use this classification of goods and construct

the empirical measure of the Import Ratio defined in Section 2.5:

Net Imports of Complex Goods + Net Exports of Basic Goods

Manufacturing Output,

where manufacturing output is the total output in the sector that produces complex goods.

As an empirical counterpart of this output we use the value added from manufacturing of

“Machinery and Transport Equipment” from the U.N.’s, International Yearbook of Industrial

Statistics.

This measure captures the extent to which a country specializes in the production of basic

commodities, as well as the extent to which a country imports complex goods. Moreover,

to the extent a country’s changing composition of output and trade over time reflects its

fluctuations in productivity this measure should also capture the variation in the country’s

productivity relative to that of its trade partners.

26

To test the first two implications of the model, we first examine how interest rates and

currency risk premiums relates to import ratios in our cross-section of currencies. Figure 6

plots the average forward returns and discounts against the average import ratio for each

country over both the Pre- and Post-Euro samples. For this figure, forward discounts and

currency returns are calculated from the perspective of the US investor. In order to focus

on cross-sectional differences in countries as opposed to time series changes, the per-period

averages of country discounts and returns are subtracted. As the first plot shows, there is a

clear relation between the import ratio and average forward discounts. Commodity countries

are generally high interest rate countries, consistent with the predictions of the model. The

second plot shows a similar pattern in returns, with the commodity countries earning higher

returns than producer countries, again consistent with the model. Notably, the U.S. is an

average country in terms of its trade composition, and also an average country in terms of

forward discounts and returns.

To test for statistical significance of these relations, Table 2 presents cross-sectional re-

gression evidence that relates our import/export composition variable to the excess currency

returns and forward discounts. Panel A presents results for the full sample of countries (IMF

Advanced Economies) while Panel B presents the results for the G10 currencies. The left hand

side of each panel presents estimates from Fama-MacBeth regressions of monthly currency

excess returns on the import ratios. The right hand side of each panel presents estimates

from Fama-Macbeth regressions of monthly forward discounts on import ratios. Standard

errors are Newey-West with 36 months of lags to account for time-series persistence in the

dependent variables.

As evidenced by the regression slope coefficients, the import ratio is a strong positive

predictor of future excess returns, and is strongly correlated with contemporaneous forward

discounts. As indicated by the R2 of this regression, our trade-based variable explains a

substantial portion of the cross-sectional variation in the average interest rate differentials

across countries, as well as in average returns. This variation is clearly not driven entirely

by country size as suggested by Hassan (2013), since the U.S. as well as the U.K. are in the

middle of the distribution of the import/export variable (as well as of the average forward

discount, which equals zero for the U.S. by construction). Controlling for the logarithm of

27

Figure 6: Import Ratios vs. Forward Discounts and FX Returns

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This figure plots forward discounts and excess FX returns against the import ratio for each country in ourIMF Advanced Economies sample. The import ratio is calculated as

Net Imports of Complex Goods + Net Exports of Basic Goods

Manufacturing Output,

Both forward discounts and FX returns are calculated from the perspective of a U.S. investor. Underlined

observations are the averages for the Pre Euro period and non-underlined observations are the average of

the Post Euro period. For each period both average returns and discounts are adjusted by subtracting the

period mean for all countries.

28

country GDP in a manner similar to Hassan (2013) shows a relation between country size and

currency risk premia subsumed by the import ratios in the full sample. In the G10 country

sample both variables are significant. Controlling for a lagged 3-year rolling average of log

CPI changes as a measure of inflation forecast weakens somewhat the predictive power of the

import ratio for the cross-section of average returns, but does not eliminate it, and inflation

itself does not seem to predict future excess returns. Inflation is strongly related to forward

discounts, but its inclusion leaves the coefficients on the import ratio largely unchanged and

highly significant for the full sample. While the power is reduced for the G10 sample, the

import ratio remains significant in all cases. This evidence is consistent with the model’s

prediction that the import ratio contains relevant information about the real interest rate

differential and currency risk premia. For countries that experienced high inflation for a

sustained period of time in our sample forward discounts are less informative about risk

premia since they are dominated by expected inflation, which on average translates into

depreciation of the high-yielding currency (e.g., Bansal and Dahlquist (2000)).

3.4 Import and Ratios and Exposure to Global Output

Having shown that the implications of the model regarding interest rates and currency returns

are strongly supported by the data, we now turn to the mechanism of the model. The

basic intuition of the model lies in the fact that producer countries are by their nature more

exposed to changes in global output, and that they imperfectly share this risk with commodity

countries. To test the implication that changes in producer country covary more strongly

with changes in global output, we regress growth in country productivity for the OECD

countries in our sample against growth in total OECD output. As a proxy for productivty

we use the index of real labor productivity from the OECD. Figure 7 shows slope coefficients

of these regressions plotted against the Import Ratio of each country. As the figure shows,

commodity countries such as Australia, New Zealand, and Norway have much lower exposure

to changes in global output. Across the sample of OECD countries this relation is strongly

significant, suggesting that commodity country output is indeed less important for the global

real business cycle than producer country output. Notably, the USA is an average country by

this measure as well, suggesting again that this result is not mechanically driven by country

29

Table 2: Cross-Sectional Regressions of FX Returns and Forward Discounts

Panel A: IMF Advanced Economies

Fama-Macbeth Regressios of FX Returns Fama-Macbeth Regressions of Forward DiscountsVARIABLES FX Ret FX Ret FX Ret FX Ret FX Ret Fwd Dsct Fwd Dsct Fwd Dsct Fwd Dsct Fwd Dsct

Import Ratio 0.29* 0.25* 0.25* 0.20+ 0.23** 0.23** 0.14** 0.13**(0.12) (0.12) (0.12) (0.11) (0.03) (0.04) (0.03) (0.03)

Log GDP -0.65** -0.33 -0.29 -0.30** -0.03 -0.04(0.25) (0.20) (0.21) (0.04) (0.06) (0.04)

Inflation 0.22 0.20 0.29** 0.30**(0.21) (0.22) (0.04) (0.04)

Constant 0.65 10.25* 5.17 -0.08 4.03 0.04 4.51** 0.36 -1.75** -1.17(1.31) (4.31) (3.69) (2.25) (4.18) (0.50) (0.57) (1.04) (0.62) (0.92)

Obs 4,542 4,542 4,542 4,542 4,542 4,550 4,550 4,550 4,550 4,550R-squared 0.13 0.07 0.18 0.22 0.26 0.27 0.05 0.29 0.49 0.51

Number of Months 304 304 304 304 304 304 304 304 304 304

Panel B: G10 Currencies

Fama-Macbeth Regressios of FX Returns Fama-Macbeth Regressions of Forward DiscountsVARIABLES FX Ret FX Ret FX Ret FX Ret FX Ret Fwd Dsct Fwd Dsct Fwd Dsct Fwd Dsct Fwd Dsct

Import Ratio 0.31* 0.24* 0.33** 0.20+ 0.27** 0.21** 0.14** 0.07+(0.13) (0.12) (0.13) (0.11) (0.03) (0.05) (0.04) (0.04)

Log GDP -0.90* -0.43 -0.55 -0.65** -0.26* -0.27**(0.42) (0.39) (0.41) (0.08) (0.11) (0.09)

Inflation 0.14 0.12 0.32** 0.35**(0.23) (0.24) (0.06) (0.08)

Constant 0.61 14.08* 6.88 0.50 8.67 -0.12 9.54** 3.54+ -1.99** 1.76(1.32) (6.92) (6.50) (2.40) (7.11) (0.48) (1.35) (1.93) (0.60) (1.36)

Obs 3,047 3,047 3,047 3,047 3,047 3,048 3,048 3,048 3,048 3,048R-squared 0.16 0.14 0.26 0.29 0.39 0.40 0.21 0.46 0.59 0.64

Number of Months 304 304 304 304 304 304 304 304 304 304

Newey-West Standard Errors in Parentheses** p<0.01, * p<0.05, + p<0.10

This table shows cross-sectional regressions of FX returns and forward discounts on the Import ratio as wellas log of GDP and lagged 3-year inflation. Regressions are monthly using the previous calendar year’s valuesof the independent variables. Fama-Macbeth standard errors are calculated using the Newey-West methodwith 36 lags. Data are monthly from 1988 to 2012.

30

Figure 7: Import Ratios and Exposure to Global Output Growth

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This figure plots each country’s slope coefficient from the regression

∆Productivityi,t = βi(∆GlobalOutputt) + εt

against the country’s Import Ratio. Here Productivityi,t is real labor productivity for country i taken from

the OECD, and GlobalOutputt is real output growth for the full OECD. The Import Ratio is calculated as in

Figure 6. The trend line is from a regression of country β on country Import Ratio. The regression equation

is also reported with OLS standard errors in parentheses.

size.

3.5 Real Exchange Rates and Relative Productivity

Another key implication of our model mechanism is the tight link between real exchange rates

and productivity differentials in the final-good sectors across countries. In order to test this

prediction we construct measures of real exchange rates and relative productivities for the key

“commodity” and “producer” countries vis-a-vis their main trading partners (based on the

imports and exports data). We consider the four commodity countries against their primary

31

trading partners: Australia vs. Japan; Canada vs. Germany and Japan; New Zealand vs.

Japan; and Norway vs. Germany, Japan, and Sweden.

It is difficult to construct a proxy for complex good manufacturing productivity at high

frequencies, so as a proxy we again use quarterly data on aggregate labor productivity from

the OECD. 13 The real exchange rate for each country is first calculated with respect to the

U.S. (or equivalently any base currency) for each country i as CPI i × Qi/CPIUS, where

CPI data and currency values for each country are again from the OECD, where Qi is

the nominal exchange rate of country i in the units of US dollars. Countries’ productivity

and exchange rate series are aggregated in baskets by taking logs of the (equal weighted)

geometric averages across countries. Relative productivities are then the differences of the

two baskets’ (“producer” and “commodity”) average productivities. Figure 8 depicts the

relative productivity differentials and real exchange rates for the four commodity countries

and their producer country trading partners. In all of the cases the relative productivity

measure appears to comove quite strongly with the real exchange rate.

Table 3.5 presents the results of regressions of the exchange rates between commodity

and finished good producer-countries. Panel A presents evidence from regression of changes

in average relative productivity over one or two quarters on the change in the correspond-

ing basket real exchange rate over the same quarter, or the first quarter in the case of the

two quarter specification. The latter approach is meant to capture time-aggregation of the

underlying productivity series. The regression coefficients are always positive, and statisti-

cally significant in all cases with the exception of Norway. The R2’s are also quite sizeable,

ranging between 5% and 20%, which suggests that relative productivity differentials comove

with real exchange rates in a way consistent with our model’s predictions. Panel B reports

results for differences of real exchange rates and productivity ratios. While the raw regression

coefficients are only robustly positive in the case of Norway vis-a-vis the group of its main

trading partners, when a time trend is included, the slope coefficients are positive and highly

statistically significant for the other countries, indicating strong comovement between real

exchange rates and productivity differentials.

13In Section ?? of the appendix we also report similar analysis for levels of manufacting output using theadjusted “Production in total manufacturing” quantity index from the OECD. The results are qualitativelyunchanged.

32

Table 3: Real Exchange Rates and Relative Productivity: G10 Countries

Panel A: Innovations

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

∆RPt,t+1 ∆RPt,t+2 ∆RPt,t+1 ∆RPt,t+2 ∆RPt,t+1 ∆RPt,t+2 ∆RPt,t+1 ∆RPt,t+2

∆RERt,t+1 0.044** 0.085** 0.051** 0.101** 0.037 0.078 0.075** 0.117**(0.015) (0.032) (0.013) (0.027) (0.042) (0.066) (0.019) (0.037)

Constant -0.000 -0.001 -0.001 -0.001 0.001 0.002 -0.000 -0.001(0.001) (0.002) (0.001) (0.001) (0.002) (0.002) (0.002) (0.002)

Obs. 104 103 91 90 75 74 104 103

R2 0.052 0.107 0.114 0.203 0.018 0.049 0.090 0.126

Panel B: Levels

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

RPt RPT RPt RPT RPt RPT RPt RPT

RERt -0.024 0.115** 0.018 0.084** 0.139** 0.013 0.030 0.074**(0.047) (0.022) (0.018) (0.015) (0.043) (0.065) (0.024) (0.022)

Trend -0.002** -0.001** 0.001* -0.001**(0.000) (0.000) (0.001) (0.000)

Constant 0.120 -0.355** -0.039 -0.120** -0.086** -0.139** -0.118 -0.260**(0.194) (0.086) (0.037) (0.025) (0.015) (0.028) (0.097) (0.083)

Obs. 105 105 92 92 76 76 105 105

R2 0.015 0.795 0.056 0.609 0.424 0.552 0.061 0.345

Standard errors in parentheses** p<0.01, * p<0.05, + p<0.10

This table shows regressions of relative productivity (RPt) against real exchange rates (RERt). Each com-modity country’s exchange rate and relative productivity (the log difference of producer country and com-modity country productivities) is calculated with respect to an equal weighted basket of its primary tradingpartners among the producer countries. Germany’s exchange rate is calculated using the Euro post 1999. Allexchange rates are converted to real using the relative value of the country CPI. Data are Quarterly. Panel Ashows regressions of changes in relative productivity against changes in the real exchange rate. Each countryincludes two specifications, the first is of contemporaneous quarterly changes in relative productivity againstcontemporaneous changes in the real exchange rates, and the second is the sum of the contemporaneousquarter and the next quarter’s change in relative productivity against this quarters change in real exchangerates to account for time-aggregation. Panel B shows regressions of levels of relative productivity against thelevel of the real exchange rate, both with and without and a time-trend. Relative productivity is calculatedas the log-difference of real labor productivity from the OECD. Data are Quarterly. Newey-West standarderrors with 4 lags are shown in parentheses.

33

Figure 8: Real Exchange Rates and Relative Productivity

-0.1

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0

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g R

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ea

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xch

an

ge

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te

Australia / Japan

Real Exchange Rate

Relative Labor Productivity

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Canada / Germany, Japan

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Q1-1986

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New Zealand / Japan

-0.1

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0

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Q1-2013

Norway / Germany, Japan, Sweden

3.6 Relative Productivity and Real Interest Rate differentials

The model also predicts that the movement in the real interest rate differentials is also driven

by relative productivity, since it is the only state variable in our model. Indeed, Figure 9

demonstrates that a measure of real interest rate differentials for the pairs of countries de-

scribed above, here constructed using a four-quarter moving average of inflation centered at

the current observation as in Edison and Pauls (1993), comoves very closely with the corre-

sponding relative productivity variable. Table 3.6 presents corresponding regression results.

For all of the countries excluding Norway, the relationship between relative productivity and

real interest rate differentials is strong and significant either in innovations or in levels.

3.7 Currency portfolios sorted on Import/Export data

In order to examine the patterns of average excess returns predicted by the model, we sort

all of the countries in our sample into 5 portfolios (4 for the subsample of G10 countries)

using the lagged import ratio. Specifically, in the beginning of January for each year t we

34

Table 4: Real Interest Rate Differentials and Relative Productivity: G10 Countries

Panel A: Innovations

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

∆RPt,t+1 ∆RPt,t+2 ∆RPt,t+1 ∆RPt,t+2 ∆RPt,t+1 ∆RPt,t+2 ∆RPt,t+1 ∆RPt,t+2

∆RIRt,t+1 0.331 0.711* 0.061 0.658* -0.317 -0.088 0.299 0.934**(0.242) (0.349) (0.222) (0.293) (0.247) (0.289) (0.366) (0.256)

Constant -0.000 -0.001 -0.000 -0.001 0.001 0.002 -0.000 -0.000(0.001) (0.002) (0.001) (0.001) (0.002) (0.002) (0.002) (0.002)

Obs. 101 101 88 88 72 72 101 101

R2 0.016 0.043 0.001 0.065 0.015 0.001 0.014 0.080

Panel B: Levels

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

RPt RPt RPt RPt RPt RPt RPt RPt

RIRt 2.680** 1.380** 1.607** 1.826** -0.371 -0.283 0.805* 0.567(0.804) (0.487) (0.201) (0.243) (1.026) (0.862) (0.382) (0.473)

Trend -0.001** 0.000 0.001** -0.000(0.000) (0.000) (0.000) (0.000)

Constant -0.012 0.069** 0.151** 0.324** 0.066 0.325* 0.075* 0.255**(0.040) (0.040) (0.038) (0.078) (0.080) (0.146) (0.036) (0.095)

Obs. 101 101 89 89 73 73 101 101

R2 0.181 0.626 0.486 0.503 0.003 0.500 0.076 0.124

Standard errors in parentheses** p<0.01, * p<0.05, + p<0.10

This table shows regressions of relative productivity (RPt) on real interest rate differentials (RIRt) . Eachcommodity country’s relative interest rate and relative productivity is calculated with respect to an equalweighted basket of its primary trading partners among the producer countries as in Table 3.5. Germany’sinterest rate is calculated using the Euro post 1999. All interest rates are converted to real by adjusting forpredicted inflation calculated as a four quarter moving average of CPI growth centered at the observation.Data are quarterly. Newey-West standard errors with 4 lags are shown in parentheses.

35

Figure 9: Real Interest Rates and Relative Productivity

-0.2

-0.15

-0.1

-0.05

0

0.05

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0.15

0.2

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0

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0.05

Q1-1986

Q1-1989

Q1-1992

Q1-1995

Q1-1998

Q1-2001

Q1-2004

Q1-2007

Q1-2010

Q1-2013

Lo

g R

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tive

Pro

du

ctio

n /

Pro

du

ctivity

Re

al In

tere

st

Ra

te D

iffe

ren

tia

l

Australia / Japan

Real Intereset Rate Differential

Relative Labor Productivity

-0.05

-0.04

-0.03

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0

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Q1-1986

Q1-1989

Q1-1992

Q1-1995

Q1-1998

Q1-2001

Q1-2004

Q1-2007

Q1-2010

Q1-2013

Canada / Germany, Japan

-0.15

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0

0.05

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0.15

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0

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Q1-1986

Q1-1989

Q1-1992

Q1-1995

Q1-1998

Q1-2001

Q1-2004

Q1-2007

Q1-2010

Q1-2013

New Zealand / Japan

-0.13

-0.08

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0

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Q1-1986

Q1-1989

Q1-1992

Q1-1995

Q1-1998

Q1-2001

Q1-2004

Q1-2007

Q1-2010

Q1-2013

Norway / Germany, Japan, Sweden

sort currencies based on the export ratio that is based on the trade data for the year t− 2.

This is because countries report their trade statistics to COMTRADE slowly, sometimes with

complete reports available only by the end of the following year.

The construction of these portfolios represents an implementable trading strategy, rely-

ing only on trade data from available at the time of portfolio formation. Average forward

discounts and average returns are computed from 1988-2012.

We work with one-month forward and spot exchange rates in units of foreign currency

per U.S. dollar, denoted by Ft and St, respectively. Using the individual currency one-month

forward discounts ft − st (lower case letters representing logarithms) and log excess returns

approximated as

rxt+1 = ft − st+1,

we compute the log currency excess return rxjt+1 for each portfolio j = 1, 2 . . . , 6 by averaging

36

over Nj currencies in the portfolio:

rxjt+1 =1

Nj

∑i∈Nj

rxit+1. (21)

Similarly, currency portfolio excess returns (in levels) RXj are computed by averaging indi-

vidual currency excess returns in levels, RX i = (F it − Sit+1)/Sit analogously to (21). We do

not take into account bid/ask spreads in the construction of these portfolios at the monthly

frequency. Since our portfolios require very little rebalancing, transaction costs are likely to

be small (returns based on long-horizon, e.g. one-year, forward contracts are typically sim-

ilar to those obtained by rolling over shorter-horizon contracts; we report the results using

one-year forward contracts with bid-ask spreads in the Data Appendix.).14

The results are reported in Panel I of Table 5. The results using both sorts are very

similar: portfolios representing large complex good exports and basic good imports relative

to their output have low average forward discounts, suggesting that they capture countries

whose interest rates are typically low relative to the U.S. Conversely, portfolios with high

values of commodity exports and low values of final good exports exhibit high average forward

discount, indicating high average interest rates. The pattern is virtually monotonic across

portfolios, especially for developed countries subsample, with differences between the highest

and the lowest portfolios’ average forward discounts of around 4% per annum for the basic

good sort over 5% per annum for the complex good sort.

Importantly, portfolio average excess returns follow the pattern of the average forward

discounts, being negative for the low portfolios and positive for the high portfolios, with the

spreads in average returns between extreme portfolios close to 4% per year for both the basic

good sort and the complex good sort. Thus, the differences in the average forward discounts

translate almost fully into average excess returns, contrary to the UIP hypothesis. Since

the sorting variables are very persistent, these differences are likely to capture unconditional

rather than conditional risk premia. To facilitate comparison with traditional carry-trade

strategies, we sort countries based on forward discounts at the same frequency as the import-

14The portfolio is rebalanced to handle the introduction of the Euro. Prior to 1999 breakpoints arecalculated including the component countries of the Euro as separate entities. Post 1999 the breakpoints arerecalculated counting the Eurozone as a single country.

37

sorted portfolios. That is, each January we sort currencies based on their forward discount vis-

a-vis the U.S. dollar at the end of December. This puts the import sort on equal footing with

the carry-trade sort in the sense that the information used to update the portfolios arrives

at the same frequency (in both cases the portfolios are rebalanced monthly). The annual

portfolio formation period departs from the traditional method of sorting currencies based on

the current interest rate in each month as in Lustig, Roussanov, and Verdelhan (2011). The

resulting annual sort displays somewhat less variation in average forward discounts across

portfolios and a narrower spread in average excess returns that the month sort as in Lustig,

Roussanov, and Verdelhan (2011). Average forward discounts and excess returns for these

portfolios are shown in Panel II of Table 5. Both the spread in the average forward discounts

and that in average excess returns are essentially of the same magnitude as those in the

obtained using the import ratio sort in Panel I.

3.8 Explaining the carry trade with IMX factor

Lustig, Roussanov, and Verdelhan (2011) show that carry-sorted exhibit strong factor struc-

ture that implies heterogeneity in countries’ SDFs exposures to a global source of risk, which

is corroborated by the fact that average returns on carry portfolios line up with loadings

on a common factor. If our model is a good description of such heterogeneity in risk expo-

sures then import-sorted portfolios should exhibit similar properties. As a candidate for the

risk factor capturing global SDF shocks we consider returns on a portfolio which is long the

portfolio with the highest import ratio and short the lowest import ratio. We refer to this

strategy as IMX (Importers Minus eXporters of finished goods).

Table 6 present results of standard asset pricing tests using both the full sample of coun-

tries and the smaller G10 sample. Panel lists displays cross-sectional estimates of the IMX

market price of risk λIMX and the corresponding SDF loading bIMX using both the SDF-

GMM methodology and the Fama-MacBeth approach, together with the cross-sectional pric-

ing error tests. Panel II lists estimated time-series estimates of factor loadings βiIMX for each

portfolio as well as the pricing error αi0, as well as the joint test statistics for the alphas.

The tests show that the prices of risk and factor loadings, while imprecisely estimated (given

the relatively short length of the sample) are nevertheless statistically significant using most

38

Table 5: Currency Portfolios Sorted on Combined Imports/Exports Measure

Portfolio 1 2 3 4 5 1 2 3 4

Panel I: Portfolios Sorted on Import RatiosAll Countries G10 Countries

Forward Discount: f j − sj f j − sjMean −0.45 −0.41 0.70 0.67 2.58 −1.93 0.42 1.24 2.52

Std 0.73 0.66 0.78 0.60 0.52 0.70 0.71 0.51 0.54

Log Excess Return: rxj rxj

Mean −0.95 0.36 0.84 0.96 3.76 −0.87 0.36 1.38 3.49Std 8.57 11.11 8.42 7.73 9.67 9.56 10.80 7.08 9.69SR −0.11 0.03 0.10 0.12 0.39 −0.09 0.03 0.20 0.36

Excess Return: Rxj Rxj

Mean −0.36 1.03 1.30 1.40 4.41 −0.24 1.00 1.77 4.14Std 8.55 11.09 8.36 7.69 9.62 9.58 10.75 7.03 9.64SR −0.04 0.09 0.16 0.18 0.46 −0.02 0.09 0.25 0.43

Panel II: Portfolios Sorted on Forward DiscountsAll Countries G10 Countries

Forward Discount: f j − sj f j − sjMean −2.30 −0.67 0.66 1.61 3.78 −2.18 −0.02 1.28 3.51

Std 0.64 0.57 0.58 0.69 0.81 0.63 0.50 0.61 0.78

Log Excess Return: rxj rxj

Mean −0.24 1.33 3.32 2.81 4.07 −0.28 2.80 2.58 4.24Std 9.45 9.62 9.59 8.71 10.27 10.04 8.51 8.89 10.29SR −0.03 0.14 0.35 0.32 0.40 −0.03 0.33 0.29 0.41

Excess Return: Rxj Rxj

Mean 0.33 1.91 3.86 3.32 4.79 0.38 3.27 3.08 4.96Std 9.47 9.64 9.60 8.65 10.20 10.09 8.49 8.84 10.23SR 0.04 0.20 0.40 0.38 0.47 0.04 0.39 0.35 0.48

This table reports average forward discounts and average (log and level) excess returns on currency

portfolios sorted on the Import Ratio (panel I) and on log forward discounts (panel II). The Import

Ratio is constructed by adding the level of net exports in basic goods to the level of net imports in

finished goods, and then dividing by the level of manufacturing output of the country, as prescribed

by the model. The rankings are updated at the end of each using the prior year’s trade data

or current forward discounts. Trade data are annual, from UN Comtrade (available via NBER

extracts). Forward and spot exchange rate data are monthly, from Barclays and Reuters (available

via Datastream). The returns do not take into account bid-ask spreads. The sample period is

2/1988 to 4/2013.

39

methods and are broadly consistent in magnitudes with the mean of the IMX factor (4.53%

in the full sample and 4.11% in the G10 sample. More importantly, the pricing errors are

not statistically significant either individual or jointly using any method. Factor betas are

essentially monotonically increasing in the import ratio. This evidence is consistent with the

notion that the spread in average returns on import-sorted portfolios is driven by differences

in exposures to a common source of risk captured by the IMX strategy.

Table 6 presents similar evidence but now using the carry-sorted portfolios as the test

assets for the IMX factor. At the level of individual portfolios the factor betas exhibit the

same monotonic pattern, increasing with interest rate differential. Individual pricing errors

are not statistically significantly different from zero, and are jointly at only at 10% level (p-

value of 9.32%) in the full sample. The implied prices of risk are somewhat larger (but not

statistically significantly so). This is potentially due to the somewhat smaller spread in betas,

indicating potential measurement error problems stemming either from the mismeasurement

of real interest rate differentials using forward discounts or, more likely, of the import ratios

constructed using trade data. This evidence broadly indicates, however, that the import-

sorted and carry-sorted portfolios share a common source of risk that drives heterogeneity in

average returns, consistent with the model’s predictions.

3.9 Case study: the global financial crisis

As a further illustration of the model mechanisms in the data, we examine the behavior of

model variables during the global financial crisis, which coincided with a dramatic decline

in output, especially among final-good producer countries, such as Japan, and a collapse

in international trade volume (e.g. see Eaton, Kortum, Neiman, and Romalis (2011)). As

Figure 10 shows, the data lines up nicely with the model predictions over this period. Panel

A shows that the commodity currencies tended to depreciate relative to final-good producer

currencies during the crisis. Panel B illustrates that this is reflected in a large negative return

on the IMX strategy, and that this return is accompanied by large negative changes in the

CRB Commodity Spot Index and the Baltic Dry Index. Perhaps most importantly, even

though commodity prices were dropping during this period, Panel C shows the productivity

of the commodity countries did not fall as severely as that of the producer countries. The

40

Table 6: Asset Pricing Tests: Portfolios Sorted by Import Ratio

Panel I: Risk Prices

All Countries G10 Countries

λIMX bIMX R2 RMSE χ2 λIMX bIMX R2 RMSE χ2

GMM1 5.71 0.65 37.71 1.16 4.70 0.43 −12.59 1.58

[3.23] [0.37] 68.19 [2.89] [0.27] 55.03

GMM2 4.50 0.51 29.67 1.23 4.31 0.40 −13.52 1.59

[2.00] [0.23] 74.92 [2.35] [0.22] 55.59

FMB 5.71 0.65 86.92 1.16 4.70 0.43 83.98 1.58

[2.37] [0.27] 73.62 [2.05] [0.19] 48.21

[2.39] [0.27] 74.93 [2.05] [0.19] 49.12

Mean 4.53 4.11

Panel II: Factor Betas and Pricing Errors

All Countries G10 Countries

Portfolio αj0 βjIMX R2 χ2(α) p− val αj0 βjIMX R2 χ2(α) p− val1 1.52 −0.36 13.18 2.03 −0.49 23.46

[1.70] [0.08] [1.80] [0.08]

2 0.93 0.09 0.54 1.03 0.06 0.26

[2.34] [0.11] [2.45] [0.12]

3 1.31 0.05 0.23 0.95 0.21 8.34

[1.84] [0.09] [1.51] [0.08]

4 0.63 0.20 5.06 2.03 0.51 25.60

[1.71] [0.09] [1.80] [0.08]

5 1.52 0.64 32.39

[1.70] [0.08]

1.80 87.60 2.17 70.53

Notes: The panel on the left reports results for all countries in our sample. The panel on the right reportsresults for the G10 group of developed countries with most widely-traded currencies. Panel I reports resultsfrom GMM and Fama-McBeth asset pricing tests. Market prices of risk λ, the adjusted R2, the square-root ofmean-squared errors RMSE and the p-values of χ2 tests on pricing errors are reported in percentage points.b denotes stochastic discount factor loadings on the IMX strategy return. All excess returns are multipliedby 12 (annualized). Shanken (1992)-corrected standard errors are reported in parentheses. We do not includea constant in the second step of the FMB procedure. Panel II reports OLS estimates of the factor betas andalphas (pricing errors) for each of the portfolios. R2s and p-values are reported in percentage points. Thestandard errors in brackets are Newey and West (1987) standard errors computed with the optimal numberof lags according to Andrews (1991). The χ2 test statistic α′V −1α α tests the null that all intercepts are jointlyzero. This statistic is constructed from the Newey-West variance-covariance matrix (1 lag) for the system ofequations (see Cochrane (2005), p. 234). Data are monthly, from Barclays and Reuters in Datastream. Thesample period is 2/1988–4/2013. The alphas are annualized and in percentage points.

outliers are two of the smaller countries within each group, New Zealand and Switzerland.

Panel D shows that a GDP-weighted basket of commodity countries’ productivity greatly

outperforms that of final-goods producers during the crisis.

41

Figure 10: Currencies, Commodities, Trade Costs, and Productivity During the Crisis

0.6

0.8

1

1.2

Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10

Panel A: G-10 Currencies

AUD CAN

NOK NZD

EUR JPY

SWE CHE

0

3000

6000

9000

12000

15000

0.5

0.7

0.9

1.1

1.3

1.5

Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10

BD

I

Panel B: Commodities, Trade Costs, and IMX

IMX

CRB Spot Commodity Index

Baltic Dry Index

0.85

0.87

0.89

0.91

0.93

0.95

0.97

0.99

1.01

1.03

1.05

2007 2008 2009 2010 2011

Panel C: G-10 Productivity

Australia

Canada

New Zealand

Norway

Euro Area

Japan

Switzerland

Sweden0.94

0.96

0.98

1

1.02

2007 2008 2009 2010 2011

Panel D: G-10 GDP-Weighted Productivity

Commodity Countries

Producer Countries

Currency and economic variables during the global financial crisis. Panel A shows monthlycumulative currency returns on the four G10 ”commodity countries” (Australia, Canada, NewZealand, and Norway) and the four G10 ”producer countries” (Europe, Japan, Switzerland,and Sweden). Panel B shows the monthly performance of the IMX strategy as well as monthlychanges in the Commodity Research Bureau All Commodity spot index and the Baltic DryIndex (BDI). Panel C shows the productivity growth of the eight countries, and Panel Dshows the productivity growth of GDP-weighted baskets of the two country groups. Allexchange rate, commodity price, and consumption variables normalized to one in December2007. Data from Datastream and the OECD.

42

Table 7: Asset Pricing Tests: Portfolios Sorted by Forward Discounts

Panel I: Risk Prices

All Countries G10 Countries

λIMX bIMX R2 RMSE χ2 λIMX bIMX R2 RMSE χ2

GMM1 10.58 1.20 78.20 1.21 7.84 0.72 56.64 1.67

[7.17] [0.81] 61.94 [4.06] [0.38] 21.54

GMM2 12.12 1.38 75.87 1.27 6.20 0.57 52.09 1.75

[4.43] [0.50] 64.07 [3.20] [0.30] 24.03

FMB 10.58 1.20 78.21 1.21 7.84 0.72 75.48 1.67

[4.21] [0.48] 13.42 [2.56] [0.24] 11.30

[4.43] [0.50] 18.19 [2.60] [0.24] 12.99

Mean 4.53 4.11

Panel II: Factor Betas and Pricing Errors

All Countries G10 Countries

Portfolio αj0 βjIMX R2 χ2(α) p− val αj0 βjIMX R2 χ2(α) p− val1 −0.78 −0.22 4.27 0.54 −0.43 19.16

[1.84] [0.08] [1.83] 0.09

2 −1.75 0.11 1.11 −0.63 0.11 1.36

[1.95] [0.10] [1.86] 0.08

3 1.58 0.15 2.06 2.69 0.22 5.35

[1.99] [0.09] [1.93] 0.09

4 2.31 0.23 5.15 3.04 0.44 16.66

[1.88] [0.09] [2.07] 0.09

5 2.81 0.44 13.46

[2.16] [0.11]

9.43 9.32 7.02 13.48

Notes: The panel on the left reports results for all countries in our sample. The panel on the right reportsresults for the G10 group of developed countries with most widely-traded currencies. Panel I reports resultsfrom GMM and Fama-McBeth asset pricing tests. Market prices of risk λ, the adjusted R2, the square-root ofmean-squared errors RMSE and the p-values of χ2 tests on pricing errors are reported in percentage points.b denotes stochastic discount factor loadings on the IMX strategy return. All excess returns are multipliedby 12 (annualized). Shanken (1992)-corrected standard errors are reported in parentheses. We do not includea constant in the second step of the FMB procedure. Panel II reports OLS estimates of the factor betas andalphas (pricing errors) for each of the portfolios. R2s and p-values are reported in percentage points. Thestandard errors in brackets are Newey and West (1987) standard errors computed with the optimal numberof lags according to Andrews (1991). The χ2 test statistic α′V −1α α tests the null that all intercepts are jointlyzero. This statistic is constructed from the Newey-West variance-covariance matrix with 1 lag. Data aremonthly, from Barclays and Reuters in Datastream. The sample period is 2/1988–4/2013. The alphas areannualized and in percentage points.

3.10 Conditional Asset Pricing Implications

The evidence on cross-sectional behavior of expected currency excess returns based on the as-

set pricing tests reported in Section 3.8 above is consistent with the unconditional implications

43

of our model (commodity currency is riskier on average) as well as its conditional implica-

tions. The latter is because variation in a country’s import ratio over time determines which

portfolio it is sorted into, so that unconditional betas at the portfolio level capture condi-

tional covariances of individual currencies with the IMX factor (Cochrane (2011) stresses this

interpretation of the cross-sectional evidence in Lustig, Roussanov, and Verdelhan (2011)).

However, these tests do not fully exploit our model’s predictions for the conditional expected

returns on the currency carry trade. Specifically, implication (3) in Section 2.7 suggests that

the conditional expected returns on the IMX strategy should vary over time, being higher

when relative productivity of commodity countries relative to producer countries is greater,

and lower otherwise.

Testing this prediction is complicated by the fact that both our relative productivity

measure and the import ratio that proxies for relative productivity according to the model are

time-aggregated at annual frequency. As a consequence, they make for very noisy instruments

for summarizing conditioning information available at a particular point in time, especially for

capturing conditional expected returns that vary over relatively short horizons. Fortunately,

we can exploit our model’s predictions for the behavior of trade/shipping costs to use variables

that are observed at a particular point in time, as suggested by equation (12). In particular,

we can use the Baltic Dry Index (BDI) of the spot freight rates for dry bulk goods available

from the Baltic Exchange as a proxy for trade costs. While the model notion of trade costs

is wider than just the costs of shipping, to the extent that shipping costs increase with the

amount of goods exported, as the supply of ships is inelastic in the short run, they serve

as a good proxy for the relative productivity that is not observed at high enough frequency.

Given the highly persistent nature of the BDI variable, we use its monthly growth rate,

∆BDIt+1 = BDIt+1

BDItas the conditioning variable in order to reduce the possibility of small-

sample bias associated with persistent predictors.

In order to test the conditional implications of our model we expand the set of test

assets by augmenting it with returns on “managed portfolios”; i.e. test portfolio returns

“scaled” by the conditioning variable, R̃xt+1 = Rxt+1 ⊗ zt, where zt is the conditioning

variable (in the GMM context this amounts to enlarging the set of moment conditions by

instrumenting using zt, e.g. as introduced in Hansen and Singleton (1982). We also allow the

44

price of risk associated with IMX estimated in the cross-sectional regression to depend on the

conditioning variable, so that λIMXt = λ0 + λ1∆BDIt, which is equivalent to expanding the

the set of priced factors in the SDF to ft+1 = [IMXt+1,∆BDIt×IMXt+1]. This approach to

testing conditional asset pricing models using scaled factors in conjunction managed portfolios

is advocated by Cochrane (1996)). Nagel and Singleton (2010) develop a procedure that

maximizes the power of the conditional tests, while Roussanov (2014) incorporates flexible

nonparametric estimation of the conditional prices of risk. Here we pursue the standard

approach for simplicity.

We present the results of our conditional tests in Table 8. We consider two sets of test

assets separately: those based on the Import ratio sort and on the forward discount (Carry)

sort. The first five test assets (numbered 1-5) in each set are the original sorted portfolios,

while the remaining portfolios (6-10) are the original ones scaled with ∆BDIt. Panel I

reports the price of risk and SDF factor loadings together with the cross-sectional tests using

either the GMM or the Fama-Macbeth methodology (p-values for the appropriate χ2 test

statistic are reported in each case). Panel II reports the time-series regression results for each

portfolio (alphas, betas, and R2) as well as the cross-sectional GRS tests. For the import-

sorted portfolios both λ0 and λ1 are positive and statistically significant, indicating that not

only is IMX priced in the cross-section of currency returns, but its price of risk varies over

time with shipping costs, as predicted by the model. Their magnitudes are also consistent

with the average returns on the corresponding factor-mimicking portfolios. The SDF factor

loadings b are generally less precisely estimated and therefore not significant except using

the (efficient) second-stage GMM, where b1 is significant. The results are similar for the

Carry-sorted portfolio; the magnitudes of risk prices are somewhat larger in this case but

not significantly different from the factor sample means. Crucially, in both cases the cross-

sectional pricing error tests fail to reject the model. This is consistent with the evidence from

portfolio-level tests where none of the alphas are statistically significantly different from zero.

45

4 Conclusion

We present new evidence on the currency carry trade: countries that specialize in exporting

basic goods such as raw commodities tend to exhibit high interest rates where as countries

primarily exporting finished goods have lower interest rates on average. These interest rate

differences translate almost entirely into average returns on currency carry trade strategies.

We propose a novel mechanism that helps rationalize these findings: comparative advantage

in production of different types of goods combined with convex trade costs and time-varying

capacity of the shipping industry. Nonlinearity of the trade costs, as well as the ability of

the commodity country to insure itself through domestic production, imply that the SDF of

the country that is more efficient at producing the consumption good is more sensitive to

productivity shocks, making its currency a “safe haven” and commodity country currency

risky. Our model’s empirical predictions are strongly supported in the data.

46

Table 8: Asset Pricing Tests with Conditioning Information

Panel I: Risk Prices

Import Sort Carry Sort

λIMX λIMX×BDI bIMX bIMX×BDI χ2 λIMX λIMX×BDI bIMX bIMX×BDI χ2

GMM1 4.94 7.66 −0.55 1.06 9.19 10.96 0.44 0.51

[1.80] [3.20] [1.41] [1.29] 20.99 [4.21] [5.65] [1.10] [1.08] 74.66

GMM2 5.45 7.79 −0.31 0.89 11.36 13.03 0.78 0.74

[1.69] [1.96] [0.38] [0.32] 23.35 [2.96] [2.84] [0.55] [0.29] 80.32

FMB 4.94 7.66 −0.55 1.06 9.19 10.96 0.44 0.51

[1.79] [2.90] [1.25] [1.14] 17.27 [3.11] [4.48] [1.00] [0.99] 60.55

[1.80] [2.94] [1.28] [1.17] 20.44 [3.22] [4.66] [1.04] [1.03] 67.24

Mean 4.60 6.67 4.60 6.67

Panel II: Factor Betas and Pricing Errors

All Countries G10 Countries

Portfolio αj0 βjIMX βIMX×BDI R2 χ2 αj0 βjIMX βIMX×BDI R2 χ2

1 1.22 −0.53 0.16 13.90 −0.86 −0.57 0.34 7.13

[1.66] [0.23] [0.17] [1.85] [0.19] [0.17]

2 0.20 −0.28 0.36 2.58 0.38 −0.12 0.12 0.34

[2.35] [0.30] [0.23] [1.86] [0.29] [0.21]

3 1.13 −0.05 0.09 0.48 1.76 −0.00 0.21 4.74

[1.84] [0.21] [0.16] [1.96] [0.28] [0.19]

4 0.62 0.20 −0.00 5.05 1.21 0.30 −0.05 6.60

[1.61] [0.24] [0.17] [1.81] [0.24] [0.18]

5 1.22 0.47 0.16 32.97 1.20 0.25 0.16 13.57

[1.66] [0.23] [0.17] [2.14] [0.28] [0.21]

6 1.37 −0.41 0.07 10.88 −1.57 −0.90 0.73 11.61

[1.71] [0.21] [0.18] [1.99] [0.40] [0.38]

7 −0.41 −0.95 1.09 15.43 0.58 −0.12 0.15 0.63

[2.48] [0.46] [0.41] [1.86] [0.13] [0.11]

8 0.55 −0.40 0.45 5.44 1.56 −0.49 0.75 13.66

[1.94] [0.22] [0.19] [2.06] [0.23] [0.19]

9 0.74 −0.21 0.40 8.71 1.09 −0.20 0.43 10.06

[1.69] [0.18] [0.15] [1.83] [0.17] [0.14]

10 1.37 −0.41 1.07 46.64 1.36 −0.59 1.03 28.04

[1.71] [0.21] [0.18] [2.13] [0.32] [0.28]

30.49 48.97

Notes: Test assets include the original portfolios (1-5) sorted on either the Import ratio or the Forwarddiscount (Carry sort) as well as the same portfolio returns scaled with the conditioning variable BDI (6-10).All excess returns are multiplied by 12 (annualized). Panel I reports results from GMM and Fama-McBethasset pricing tests. Market prices of risk λ and the p-values of χ2 tests on pricing errors are reported inpercentage points. b denotes stochastic discount factor loadings on the IMX strategy return. Shanken(1992)-corrected standard errors are reported in parentheses. We do not include a constant in the secondstep of the FMB procedure. Panel II reports OLS estimates of the factor betas and alphas (pricing errors)for each of the portfolios. R2s and p-values are reported in percentage points.

47

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52

Appendix

Additional Derivations and Proofs

Relative productivity

To focus on the countries’ relative productivities, we project the imperfectly correlated

Brownian motions dBc and dB onto each other, leaving a residual that is a stochastic inte-

gral with respect to an independent Brownian motion, Bz: more specifically, we construct

dBc = ρdBz +√

1− ρ2dB. We then define z by the equation zpz.= zcp and derive zcp as a

general process from here.

zpz.= zcp (A-1)

dzpz + zpdz + dzdzp = dzcp (A-2)

zzp(µdt+ σdB) + (µztdt+ σzdBz + dL− dU)zp = µ(zcp)dt+ σ(zcp)dBc (A-3)

= µ(zcp)dt+ σ(zcp)(ρdBz +

√1− ρ2dB

)(A-4)

We then need to solve a system of three equations for µ(zcp), σ(zcp) and ρ:

µ(zcp)dt = zµzpdt+ µztzpdt+ zpdL− zpdU

σ(zcp)ρ = σzzp

σ(zcp)√

1− ρ2 = zσzp

Solving this system we get ρ =√

σ2z

σ2z+z2σ2 , σ(zcp) = zp

√σ2z + z2σ2, and µ(zcp)dt = µztzpdt +

zµzpdt − zpdU + zpdL, where for clarity we include the regulator terms dL and dU in the

general drift term of zcp.

The projection implies an interesting result: the processes for zcp and zp are highly cor-

related when their technologies for producing the final good are similar—when zcp is close

to zp. To see this, when z increases, then ρ decreases, and thus the correlation between dBc

and dB,√

1− ρ2, increases. All together, we get a stochastic process z that takes values on

53

(z, 1):

dz = µztdt+ σzdBz − dU + dL.

Before formally defining U(t) and L(t), first define z(t) as the sum of an arithmetic

Brownian motion x(t) = x0 +∫ t

0µztdt +

∫ t0σzdBzt and the two regulators U(t) and L(t):

z(t) = x(t)−U(t) +L(t). Now define a stopping time T0 as the first date when x(t) = z with

initial condition x(0) = x0 > z:

L(t) =

0, t ≤ T0, all ω

z −mins∈[0,t] x(s), t > T0, all ω

Thus, L(t) is continuous and non-decreasing, L(0) = 0, and only increases if z(t) = z.

Now define a stopping time T1 as the first date when x(t) = 1 with initial condition

x(0) = x0 < 1:

U(t) =

0, t ≤ T1, all ω

maxs∈[0,t] x(s)− 1, t > T1, all ω

Thus, U(t) is continuous and non-decreasing, U(0) = 0, and only increases if z(t) = 1.

Construction of the stochastic processes U(t) and L(t) for two boundaries z < 1 with

initial condition x0 ∈ [z, 1] proceeds by induction, following Stokey (2009, p.202), and culmi-

nates in her Proposition 10.1 that states the regulated Brownian motion z(t) is

z(t) = x(t)− U(t) + L(t), all t,

where L(t) and U(t) are stochastic processes, and (L,U, z) have the following properties:

1. L and U are continuous and nondecreasing, with L0 = U0 = 0

2. z(t) satisfies z(t) ∈ [z, 1], all t

3. L(t) only increases when z(t) = z; U(t), when z(t) = 1

An important fact is

E[(dz)2] = E[(dx)2] = σ2zdt.

54

Because we specify the drift of the process to be non-constant (µz = σ2z/z), a closed-form

solution for the stationary density is unavailable. Instead, we bound a process from below by

0.3 and simulate a sample path of 100-million innovations and plot its histogram in Figure

11. The stationary density is tilted and has more mass near the upper boundary.

Figure 11: Histogram of simulated stationary density of relative productivity shock

0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7x 10

7

z

Proof of Lemma 1. To show this, we fix an initial condition z0 ∈ [z, 1] and define a localizing

process of stopping times 0 = τ 0 < τ 1 < τ 2 < · · · → ∞ by

τn+1 = min{t > τn|z(t) = z0 and z(s) = z and z(s′) = 1, for some τn < s, s′ < τn+1}.

Thus each stopping time is defined by having zt reach each threshold, z and 1, and then to

return to the initial condition z0. Because of the boundedness of the process, each of these

stopping times is finite with probability one and importantly

zτn = z0, for all n.

Because Ito’s lemma for regulated processes holds for all t, we can choose t = τ 1 so that

zτ1 = z0, and therefore an application of the lemma to the real exchange rate process S (and

55

using µzt = σ2z/zt) gives

0 = −∫ τ1

0

1

φ∗z2(µzdt+ σzdBz + dL− dU) +

∫ τ1

0

1

φ∗z3σ2zdt

= − 1

φ∗z2

∫ τ1

0

dL+1

φ∗

∫ τ1

0

dU −∫ τ1

0

σzφ∗z2

dBz,

where the second equality uses the fact that dL is only positive when z = z and dU is only

positive when z = 1. Taking expectations of this process conditional on our starting value

for z gives1

z2E[∫ τ1

0

dL

∣∣∣∣S0 = S(z0)

]= E

[∫ τ1

0

dU

∣∣∣∣S0 = S(z0)

].

Because this equality holds for any arbitrary starting value within the boundaries, our expec-

tation holds almost everywhere. Applying the conditional expectation operator to dSS

, given

in (14) gives

Et[dS

S

]= 0.

By definition, our localized process is a local martingale, and because the process is bounded

it is a martingale.

Proof of Lemma 2. Divide commodity exports (2.4) by zc to get

x

zc= pzcω(zc, z) +X +X

(1− κX

2zp

)ω(zc, z),

where we highlight ω(·)’s dependence on zc. We bound this ratio above by 1 and rearrange

the equation to get

1

κ(1− φ(zc)z)

(1 +

1

2(1 + φ(zc)z)

(φ(zc)

λz

)− 1γ

)≤ zc.

The left side of the equation is a function that depends on z and zc. We first maximize

the function with respect to z (by lowering z to z¯). We then define z∗c as the maximum

of the function, defining H(z∗c ). Finally, we choose zc on the right side to equal z∗c . Thus

z∗c = H(z∗c ).

Proof of Lemma 3. From the commodity country’s first-order conditions we get ycp = p(zc−

56

x). From our relationship in (3) we can write global output Y in units of the producer

country’s final good as Y = yp + ycp · S = zpx+ p(zc − x)S = zpzc; hence dY = dzp. Simply

using the dynamics of zp and zcp and calculating the covariances produces the result.

Proof of Proposition 1. First, we define for convenience a function of z

s(z).=

12κ

(1− φ∗z)2

zcφ∗z + 1

2κ(1− φ∗z)2

,

and the risk premium function

ϕ(z).= γσ2

z

1

z2

[s(z)

(1 + φ∗z)

1− φ∗z−

1− 1γ

1 + φ∗zω(z)

].

Positivity of risk premium

In the case of log utility the risk premium function ϕ becomes

ϕ(z) = σ2z

1

z2s(z)

(1 + φ∗z)

1− φ∗z. (A-5)

We set zc high enough such that φ∗ < 1 so that s(z) is always positive. The risk premium,

additionally, is also always positive.

Positivity of interest rate differential

To see that the interest rate differential is positive, note that since the real exchange rate

process is a martingale, the interest-rate differential equals the risk premium and therefore

under the same condition on φ∗ is (almost surely) positive.

Import ratio

Even though in our model the trade cost is a pure dead weight loss, in order to be consistent

with the available measures of imports and exports in our empirical work we define the import

57

ratios omitting the losses due to trade costs and specify them as

IRc.=XS + xpS

ycpS(A-6)

IRp.= −

(X + xpS

yp

)(A-7)

∆IR.= IRc − IRp =

1κ( 1φ∗z− 1) + x

zc − x+

(1− φ∗z) 1κ

+ x

x. (A-8)

Under log utility, the quantity of commodity exports becomes

x =λ

1 + λzc +

1

1 + λ

X

zp

(1 + (1− τ(X, zk))

λ

φ∗z

)(A-9)

=λ

1 + λ

[zc +

X

zp

1

λ+X

zp(1− τ(X, zk))

λ

φ∗z

](A-10)

and it is easy to see that

∂x

∂z= − λ

1 + λ

(φ∗

κλ+

1

2κ

(1

φ∗z2+ φ∗

))< 0 (A-11)

So differentiating (A-8) gives

∂∆IR

∂z=

(− 1φ∗z2κ

+ ∂x∂z

)(zc − x) +

((1φ∗z− 1)

1κ

+ x)∂x∂z

(zc − x)2+

(−φ∗

κ+ ∂x

∂z

)x−

((1− φ∗z) 1

κ+ x)∂x∂z

x2

(A-12)

=− 1φ∗z2κ

(zc − x) + ∂x∂zzc +

(1φ∗z− 1)

1κ∂x∂z

(zc − x)2−

φ∗

κx+ (1− φ∗z) 1

κ∂x∂z

x2, (A-13)

which we need to be less than zero. There are two cases in which it is: (i) x2 ≥ (zc−x)2 and (ii)

x2 < (zc−x). The first case is trivially satisfied because 1φ∗z−1 > 1−φ∗z ⇔ (1−φ∗z)2 ≥ 0.

The second case requires making zc “large enough”, requiring the following condition to hold:

zc +

(1

φ∗z− 1

)1

κ

(x

zc − x

)2

> (1− φ∗z)1

κ, (A-14)

58

which is an easier condition to satisfy than

zc > (1− φ∗z)1

κ, (A-15)

which is required by Lemma 2 and thus holds given our choice of zc > z∗c . The difference in

import ratios, therefore, is monotonically decreasing in z.

Monotonicity in z of risk premium and interest rate differential

To show monotonicity, we differentiate the risk premium function with respect to z:

ϕ′(z) = σ2z

(−2

1

z3s(z)

1 + φ∗z

1− φ∗z+

1

z2

(s′(z)(1 + φ∗z)(1− φ∗z) + 2φ∗s(z)

(1− φ∗z)2

))(A-16)

= σ2z

(1

z2s′(z)

1 + φ∗z

1− φ∗z− 2

s(z)

z3(1− φ∗z)2(1− φ∗z(1 + φ∗z))

)< 0 (A-17)

Because s′(z) < 0, This last equation holds if 1− φ∗z − (φ∗z)2 > 0, or equivalently requiring

1 > maxz∈[z,1]

zφ∗ + z2(φ∗)2 = φ∗ + (φ∗)2 or equivalently zc >(

2√5−1

αα(1− α)1−α) 1

1−α .= F (α),

by plugging in the equation for φ∗ and rearranging terms. This last function F (α) has a

maximum of 2√5−1

on α ∈ [0, 0.8651), so we restrict our choice of α to that interval and set

zc > max{ 2√5−1

, z∗c}. The choice of exporting the commodity is partially determined by the

curvature of the commodity-producing production function of the commodity country as well

as the nonlinear dynamics of the exchange rate. The second-order term (φ∗z)2 shows up (and

thus 1−φ∗z > 0 doesn’t always hold) because the equilibrium specification needs to (lightly)

restrict the curvature of this export choice to variation in z.

Because the growth of the real exchange rate dSS

follows a martingale, the monotonicity

of the risk premium function also implies that the interest rate differential is monotone in z

as well.

Cross-sectional asset pricing methodology

Let Rxit+1 to denote the average excess return in levels on portfolio i in period t + 1. All

asset pricing tests are run on excess returns in levels, not log excess returns, to avoid having

59

to assume joint log-normality of returns and the pricing kernel. In the absence of arbitrage

opportunities, this excess return has a zero price and satisfies the following Euler equation:

Et[Mt+1Rxit+1] = 0.

We assume that the stochastic discount factor M is linear in the pricing factors f :

Mt+1 = 1− b(ft+1 − µf ),

where b is the vector of factor loadings and µf denotes the factor means. This linear factor

model implies a beta pricing model: the expected excess return is equal to the factor price λ

times the beta of each portfolio βi:

E[Rxi] = λ′βi,

where λ = Σffb, Σff = E(ft−µf )(ft−µf )′ is the variance-covariance matrix of the factor, and

βi denotes the regression coefficients of the return Rxi on the factors. To estimate the factor

prices λ and the portfolio betas β, we use two different procedures: a Generalized Method of

Moments estimation (GMM) applied to linear factor models, following Hansen (1982), and

a two-stage OLS estimation following Fama and MacBeth (1973), henceforth FMB. In the

first step, we run a time series regression of returns on the factors. In the second step, we

run a cross-sectional regression of average returns on the betas (without a cross-sectional

intercept), period by period, averaging the slope coefficients to obtain estimates of λ.

60

Data Appendix

This appendix describes the details of data construction and the robustness of empirical

results.

4.1 Pairwise Returns

To show that the trading strategies are both unconditional in nature, and not driven by any

one currency pair, we present the returns of currency pairs for each combination of short a

final good producer currency and long a commodity country currency, as well as portfolios

of all commodity countries or all producer countries. Table A-1 shows the results.

4.2 Classification of goods

We assign individual goods to “Basic” (input) and “Complex” (finished) groups based on the

descriptions of 4-digit SITC (Revision 4) categories available from the U.N. Table A-2 lists

classifications aggregated at a 2-digit SITC level, with the number of 4-digit sub-categories

falling into each of the two groups. A detailed breakdown is available upon request.

4.3 Currency strategies and transaction costs

We investigate the effect of transaction costs on the profitability of trading strategies based on

the combined export/import sort. We use bid-ask quotes for forward and spot exchange rates

from Reuters. Lyons (2001) reports that bid and ask quotes published by Reuters imply bid-

ask spreads that are approximately twice as large as actual inter-dealer spreads. We assume

that net excess returns take place at these quotes. As a result, our estimates of the transaction

costs are conservative, at least from the standpoint of a large financial institution. Since our

strategy is based on sorting currencies using trade data that is available at annual frequency,

a natural approach for minimizing the transaction costs is to use one-year forward contracts.

Therefore, we compute returns on rolling one-year forward contracts, but in order to avoid

the arbitrary choice of the starting month, we construct the portfolio returns at monthly

frequency (i.e., using overlapping yearly returns). Table A-3 lists the average depreciation of

1

Table A-1: Pairwise Currency Strategy Returns

Long Leg Short LegProducer

Europe / Switzer- CountryGermany Japan Sweden land Portfolio

Australia Return 3.90 5.22* 3.20 4.25 4.14*SE (2.41) (3.10) (2.34) (2.68) (2.33)SR 0.09 0.10 0.08 0.09 0.10

Canada Return 1.82 3.14 1.12 2.17 2.06SE (2.21) (2.71) (2.16) (2.47) (2.04)SR 0.05 0.07 0.03 0.05 0.06

Norway Return 2.14* 3.46 1.44 2.49 2.38*SE (1.23) (2.66) (1.36) (1.62) (1.31)SR 0.10 0.07 0.06 0.09 0.11

New Zealand Return 3.77* 5.09* 3.07 4.12* 4.01*SE (2.18) (2.89) (2.22) (2.35) (2.08)SR 0.10 0.10 0.08 0.10 0.11

Commodity Return 2.91* 4.22 2.21 3.26* 3.15**Country SE (1.64) (2.56) (1.64) (1.96) (1.54)Portfolio SR 0.10 0.10 0.08 0.10 0.12

Robust standard errors in parentheses*** p < 0.01, ** p < 0.05, * p < 0.1

Excess mean returns and Sharpe ratios on pairwise and portfolio trading strategies for G10commodity and final producer currencies. Returns are calculated using monthly forwardreturns for a strategy going long a commodity country currency of Australia, Canada, Norway,and New Zealand (or an equal weighted portfolio of all four), and short a producer countrycurrency of Europe (or the German Deutschmark Pre-1999), Japan, Sweden, and Switzerland(or an equal weighted porftolio). White (1980) standard errors in parentheses. Data is 1988to 2012, and returns do not include transaction costs.

2

Table A-2: COMTRADE Goods Classification

Sub-categories classified asSITC Description Basic Complex

00 Live animals 13 201 Meat and meat preparations 14 002 Dairy products and eggs 10 003 Fish and fish preparations 12 004 Cereals and cereal preparations 24 005 Fruit and vegetables 25 106 Sugar, sugar preparations and honey 4 407 Coffee, tea, cocoa, spices and manufacs. thereof 10 508 Feed. Stuff for animals excl. Unmilled cereals 6 009 Miscellaneous food preparations 5 011 Beverages 0 712 Tobacco and tobacco manufactures 4 421 Hides, skins and fur skins, undressed 9 022 Oil seeds, oil nuts and oil kernels 14 023 Crude rubber including synthetic and reclaimed 5 024 Wood, lumber and cork 14 025 Pulp and paper 0 726 Textile fibres, not manufactured, and waste 32 027 Crude fertilizers and crude minerals, nes 23 028 Metalliferous ores and metal scrap 22 029 Crude animal and vegetable materials, nes 11 032 Coal, coke and briquettes 8 033 Petroleum and petroleum products 2 1134 Gas, natural and manufactured 0 435 Electric energy 0 241 Animal oils and fats 3 042 Fixed vegetable oils and fats 14 043 Animal and vegetable oils and fats, processed 5 051 Chemical elements and compounds 0 2852 Crude chemicals from coal, petroleum and gas 0 1453 Dyeing, tanning and colouring materials 0 1154 Medicinal and pharmaceutical products 0 855 Perfume materials, toilet and cleansing preptions 0 956 Fertilizers, manufactured 0 557 Explosives and pyrotechnic products 0 458 Plastic materials, etc. 0 2859 Chemical materials and products, nes 0 1361 Leather, lthr. Manufs., nes and dressed fur skins 9 562 Rubber manufactures, nes 2 1063 Wood and cork manufactures excluding furniture 2 1264 Paper, paperboard and manufactures thereof 0 1565 Textile yarn, fabrics, made up articles, etc. 0 5866 Non metallic mineral manufactures, nes 0 3967 Iron and steel 8 2668 Non ferrous metals 26 069 Manufactures of metal, nes 0 3271 Machinery, other than electric 0 2572 Electrical machinery, apparatus and appliances 0 3673 Transport equipment 0 1081 Sanitary, plumbing, heating and lighting fixt. 0 482 Furniture 0 483 Travel goods, handbags and similar articles 0 284 Clothing 0 3585 Footwear 0 289 Miscellaneous manufactured articles, nes 0 3994 Animals, nes, incl. Zoo animals, dogs and cats 2 095 Firearms of war and ammunition therefor 0 2

Each row represents a 2-digit Standard International Trade Classification category accordingto SITC Rev. 4. The classification columns show the number of 4-digit sub-categoriesclassified as each type of good (Basic or Complex). Descriptions are from the United NationsStatistics Division.

3

the currencies in each portfolio, average (log) forward discount, and average excess returns

with and without bid-ask spreads applied.

4.4 Cross-Sectional Regressions

One concern for cross-sectional empirical tests of forward discounts and returns on the various

predictor variables is the high degree of persistence in both the independent and dependent

variables of the Fama-Macbeth regressions shown in Table 2 in the text. While the regressions

attempt to control for serial correlation of the error terms by using Newey-West standard

errors, here we take the more aggressive approach of estimating panel regressions using a

between-effects specification, which is equivalent to estimating regressions of unconditional

country means of forward discounts and FX returns on unconditional means of the predictor

variables. Table A-4 shows the results. This specification ignores all information in the time

series, and therefore has less power than the specification presented in the text, however we

still find a strong relation between the Import Ratio measures and both forward discounts

and returns.

4.5 Relative Exchange and Interest Rates vs. Manufacturing Out-

put

A primary implication of the model is that the relative productivity levels in the complex

goods sector drive the real exchange rate and the interest rate differential of the two countries.

In the main text, we proxy for this level of productivity using aggregate economic labor

productivity for the two economies. Here we report regressions using quarterly changes in

the quantity index of “Production in total manufacturing” reported by the OECD. Tables

A-5 and A-6 show the results for exchange rates and interest rates respectively. As the tables

show, the results with this proxy again provide support for the model mechanism, and are if

anything stronger than the results using aggregate productivity.

4

Table A-3: One-Year Returns on Import/Export Sorted Portfolios, All Countries

Portfolio 1 2 3 4 5 6Spot Change: ∆sj (without b-a)

Mean 0.08 −0.37 −1.03 0.37 1.33 −0.50Std 6.77 9.90 9.36 8.87 9.19 9.14

Forward Discount: f j − sjMean −0.48 1.29 1.15 1.99 2.19 2.23Std 1.87 2.19 2.39 2.29 1.32 1.63

Log Excess Return: rxj (without b-a)Mean −0.56 1.66 2.18 1.61 0.86 2.73Std 7.29 9.93 9.15 8.99 9.45 9.18SR −0.08 0.17 0.24 0.18 0.09 0.30

Excess Return: rxj (without b-a)Mean 0.01 2.32 2.80 2.29 1.62 3.38Std 7.09 9.93 9.42 8.87 9.80 9.39SR 0.00 0.23 0.30 0.26 0.17 0.36

Net Excess Return: rxjnet (with b-a)Mean 0.27 2.07 2.61 2.08 1.40 3.17Std 7.16 9.93 9.39 8.84 9.78 9.38SR 0.04 0.21 0.28 0.24 0.14 0.34

High-minus-Low: rxjnet (without b-a)Mean 2.31 2.79 2.28 1.61 3.37Std 6.57 6.58 5.93 7.59 6.96SR 0.35 0.42 0.38 0.21 0.48

High-minus-Low: rxjnet − rx1net (with b-a)

Mean 1.80 2.34 1.81 1.13 2.90Std 6.58 6.58 5.95 7.60 6.92SR 0.27 0.36 0.30 0.15 0.42

Note: Portfolios are rebalanced annually. Reported returns are sampled monthly with over-lap. Sample is 1/1988-12/2012.

5

Table A-4: Cross-Sectional Regressions of FX Returns and Forward Discounts: BetweenEffects

Panel A: IMF Advanced Economies

Fama-Macbeth Regressions of FX Returns Panel Regressions of FX DiscountsVARIABLES FX Ret FX Ret FX Ret FX Ret FX Ret FX Dsct FX Dsct FX Dsct FX Dsct FX Dsct

IMX Ratio 0.30* 0.36** 0.27* 0.32** 0.23+ 0.24+ 0.14* 0.17**(0.11) (0.11) (0.11) (0.10) (0.11) (0.12) (0.05) (0.05)

Log GDP 0.19 0.46 0.53+ -0.12 0.06 0.21(0.33) (0.29) (0.26) (0.31) (0.31) (0.14)

Inflation 0.16+ 0.17* 0.36** 0.36**(0.08) (0.08) (0.04) (0.04)

Observations 4,350 4,350 4,350 4,350 4,350 4,350 4,350 4,350 4,350 4,350R-squared 0.26 0.01 0.34 0.37 0.48 0.16 0.01 0.16 0.82 0.83

Periods 304 304 304 304 304 304 304 304 304 304

Panel B: G10 Currencies

Fama-Macbeth Regressions of FX Returns Panel Regressions of FX DiscountsVARIABLES FX Ret FX Ret FX Ret FX Ret FX Ret FX Dsct FX Dsct FX Dsct FX Dsct FX Dsct

IMX Ratio 0.26** 0.18* 0.18* 0.12 0.24* 0.20+ 0.07 0.06(0.06) (0.07) (0.07) (0.07) (0.08) (0.10) (0.05) (0.06)

Log GDP -0.77** -0.42+ -0.37 -0.59+ -0.21 -0.10(0.22) (0.22) (0.20) (0.28) (0.31) (0.17)

Inflation 0.25 0.22 0.50** 0.49**(0.14) (0.13) (0.10) (0.10)

Observations 2,927 2,927 2,927 2,927 2,927 2,927 2,927 2,927 2,927 2,927R-squared 0.17 0.14 0.25 0.31 0.40 0.54 0.41 0.59 0.97 0.97

Periods 304 304 304 304 304 304 304 304 304 304

Standard errors in parentheses** p<0.01, * p<0.05, + p<0.1

This table shows cross-sectional regressions of FX returns and forward discounts on the Import ratio as wellas log of GDP and lagged 3-year inflation. Regressions are monthly using the previous calendar year’s valuesof the independent variables. Panel regressions are calculated using between time and country effects. Dataare monthly from 1988 to 2012.

6

Table A-5: Real Exchange Rates and Relative Manufacturing Output: G10 Countries

Panel A: Innovations

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1

∆RERt,t+1 0.069* 0.303** 0.151** 0.338** 0.059 0.307+ 0.118* 0.244+(0.032) (0.106) (0.038) (0.068) (0.081) (0.171) (0.057) (0.129)

Constant -0.002 -0.005 -0.001 -0.002 0.000 -0.001 -0.003 -0.006(0.003) (0.004) (0.002) (0.003) (0.002) (0.004) (0.003) (0.005)

Obs. 104 103 104 103 104 103 104 103

R2 0.025 0.187 0.114 0.211 0.011 0.130 0.052 0.111

Panel B: Levels

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

RMt RMt RMt RMt RMt RMt RMt RMt

RERt -0.163 0.165** 0.115 0.401** 0.159+ 0.154 -0.190 0.140*(0.109) (0.054) (0.126) (0.105) (0.095) (0.134) (0.126) (0.068)

Trend -0.004** -0.004** 0.000 -0.004**(0.000) (0.001) (0.001) (0.001)

Constant 0.798+ -0.320 -0.288 -0.654** -0.044 -0.045 0.845+ -0.225(0.455) (0.212) (0.264) (0.191) (0.030) (0.037) (0.506) (0.255)

Obs. 105 105 105 105 105 105 105 105

R2 0.108 0.792 0.051 0.548 0.128 0.128 0.109 0.766

Standard errors in parentheses** p<0.01, * p<0.05, + p<0.10

Table shows regressions of relative manufacturing output (RMt) against real exchange rates (RERt). Eachcommodity country’s real exchange rate and relative productivity are calculated with respect to an equalweighted basket of its primary trading partners among the producer countries. Germany’s exchange rateis calculated using the Euro post 1999. All exchange rates are converted to real using the relative value ofcountry CPI. Relative manufacturing output is calculated as the log-difference of real manufacturing outputfrom the OECD. Data are quarterly. Newey-West standard errors with 8 lags are shown in parentheses.

7

Table A-6: Real Interest Rate Differentials and Relative Manufacturing Output: G10 Coun-tries

Panel A: Innovations

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1 ∆RMt,t+1

∆RIRt,t+1 2.668+ 4.154+ 0.282 -0.829 0.641 1.229 1.615 4.396**(1.361) (2.281) (1.241) (2.371) (0.990) (2.017) (1.457) (1.544)

Constant -0.002 -0.005 -0.001 -0.000 0.001 0.000 -0.002 -0.005(0.003) (0.005) (0.002) (0.004) (0.002) (0.004) (0.003) (0.005)

Obs. 104 103 104 103 104 103 104 103

R2 0.041 0.042 0.001 0.002 0.005 0.007 0.022 0.061

Panel B: Levels

Aus vs. Jap Can vs. Ger, Jap Nor vs Ger, Jap, Swe NZ vs Jap

RMt RMt RMt RMt RMt RMt RMt RMt

RIRt 11.269* 6.576** 20.469** 15.947* 3.188 6.676+ 14.691** 5.569+(4.486) (2.068) (7.291) (6.793) (3.970) (3.517) (4.984) (2.870)

Trend -0.003** -0.001 0.001* -0.003**(0.000) (0.001) (0.001) (0.001)

Constant 0.144** 0.319** -0.034 0.046 -0.001 -0.071* 0.093** 0.285**(0.027) (0.023) (0.028) (0.058) (0.018) (0.036) (0.027) (0.033)

Obs. 105 105 105 105 105 105 105 105

R2 0.202 0.791 0.218 0.316 0.023 0.211 0.249 0.742

Standard errors in parentheses** p<0.01, * p<0.05, + p<0.10

Table shows regressions of relative manufacturing output (RMt) on real interest rate differentials (RIRt) .Each commodity country’s real interest rate differential and relative productivity are calculated with respectto an equal weighted basket of its primary trading partners among the producer countries. Germany’s interestrate is calculated using the Euro post 1999. All nominal interest rates are converted to real by adjusting forpredicted inflation calculated as a four quarter moving average of CPI growth centered at the observation.Relative manufacturing output is calculated as the log-difference of real manufacturing outputs from theOECD. Data are quarterly. Newey-West standard errors with 8 lags are shown in parentheses.

8